Mathematical Models of the Universe's Structure and Evolution:
100 MCQ Questions and Answers
1. Which equation describes the expansion of the universe?
a) Einstein field equations
b) Friedmann equations
c) Schrödinger equation
d) Maxwell's equations
Answer: b) Friedmann equations
2. The equation a(t) t^(2/3) in cosmology describes the expansion of the universe dominated ∝
by:
a) Radiation
b) Matter
c) Dark energy
d) Neutrinos
Answer: b) Matter
3. In the ΛCDM model, what does Λ represent?
a) Dark matter
b) Dark energy
c) Baryonic matter
d) Radiation
Answer: b) Dark energy
4. The Hubble-Lemaître law is expressed as v = H d. What does H represent?₀ ₀
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
5. Which equation relates the scale factor a(t) to the energy density ρ in a flat universe?
a) (da/dt)² = (8πG/3)ρa²
b) (da/dt)² = (4πG/3)ρa²
c) (da/dt)² = (2πG/3)ρa²
d) (da/dt)² = (πG/3)ρa²
Answer: a) (da/dt)² = (8πG/3)ρa²
6. The equation of state for a perfect fluid is given by p = wρc². For dark energy, what is the
value of w?
a) 0
b) 1/3
c) -1/3
d) -1
Answer: d) -1
7. In the Einstein-de Sitter model, what is the value of the density parameter Ω?
a) 0
b) 1/2
c) 1
d) 2
Answer: c) 1
8. The critical density of the universe is given by ρc = 3H²/(8πG). What does G represent?
a) Gravitational constant
b) Galactic constant
c) Growth factor
d) Guth parameter
Answer: a) Gravitational constant
9. Which equation describes the evolution of density perturbations in the linear regime?
a) Navier-Stokes equation
b) Boltzmann equation
c) Vlasov equation
d) Jeans equation
Answer: d) Jeans equation
10. The equation dΩ/dt + 2HΩ(1-Ω) = 0 describes the evolution of:
a) Hubble parameter
b) Scale factor
c) Density parameter
d) Cosmic time
Answer: c) Density parameter
11. In inflationary models, the slow-roll parameter ε is defined as:
a) ε = (M_P²/2)(V'/V)²
b) ε = (M_P²/4)(V'/V)²
c) ε = (M_P²/8)(V'/V)²
d) ε = (M_P²/16)(V'/V)²
Answer: b) ε = (M_P²/4)(V'/V)²
12. The Friedmann equation for a curved universe includes the term:
a) ka²
b) k/a²
c) ka
d) k/a
Answer: b) k/a²
13. The equation H² = H ²[Ω_r(1+z)⁴ + Ω_m(1+z)³ + Ω_k(1+z)² + Ω_Λ] represents:₀
a) Friedmann equation
b) Acceleration equation
c) Fluid equation
d) Continuity equation
Answer: a) Friedmann equation
14. The growth factor D(a) in linear perturbation theory satisfies the equation:
a) D'' + 2HD' - 4πGρD = 0
b) D'' + 3HD' - 4πGρD = 0
c) D'' + HD' - 4πGρD = 0
d) D'' + 4HD' - 4πGρD = 0
Answer: b) D'' + 3HD' - 4πGρD = 0
15. The equation of state for radiation is:
a) p = 0
b) p = ρc²/3
c) p = -ρc²
d) p = ρc²
Answer: b) p = ρc²/3
16. The Friedmann equation can be written as (H/H )² = Ω_r(1+z)⁴ + Ω_m(1+z)³ + Ω_k(1+z)² + ₀
Ω_Λ. What does z represent?
a) Redshift
b) Scale factor
c) Cosmic time
d) Curvature parameter
Answer: a) Redshift
17. The Bianchi identity in general relativity is expressed as:
a) ᵅTᵅᵝ = 0∇
b) ᵅGᵅᵝ = 0∇
c) ᵅRᵅᵝ = 0∇
d) ᵅgᵅᵝ = 0∇
Answer: b) ᵅGᵅᵝ = 0∇
18. The equation dρ/dt + 3H(ρ+p/c²) = 0 represents:
a) Friedmann equation
b) Acceleration equation
c) Fluid equation
d) Continuity equation
Answer: c) Fluid equation
19. In the FLRW metric, ds² = -c²dt² + a²(t)[dr²/(1-kr²) + r²(dθ² + sin²θ dφ²)], what does k
represent?
a) Hubble constant
b) Curvature parameter
c) Scale factor
d) Cosmic time
Answer: b) Curvature parameter
20. The equation ä/a = -(4πG/3)(ρ + 3p/c²) represents:
a) Friedmann equation
b) Acceleration equation
c) Fluid equation
d) Continuity equation
Answer: b) Acceleration equation
21. The Boltzmann equation for the distribution function f(x,p,t) is:
a) df/dt = C[f]
b) ∂f/∂t + v· f = C[f]∇
c) ∂f/∂t + v· f + F· f = C[f]∇ ∇ₚ
d) ∂f/∂t + F· f = C[f]∇ₚ
Answer: c) ∂f/∂t + v· f + F· f = C[f]∇ ∇ₚ
22. The equation H(t) = ȧ(t)/a(t) defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: b) Hubble parameter
23. In the Einstein field equations, Gᵅᵝ = (8πG/c⁴)Tᵅᵝ, what does Tᵅᵝ represent?
a) Einstein tensor
b) Stress-energy tensor
c) Ricci tensor
d) Metric tensor
Answer: b) Stress-energy tensor
24. The equation δ = (ρ - ρZ)/ρZ defines:
a) Density contrast
b) Density parameter
c) Critical density
d) Energy density
Answer: a) Density contrast
25. The Friedmann equation for a flat universe with only matter and dark energy is:
a) H²/H ² = Ω_m(1+z)³ + Ω_Λ₀
b) H²/H ² = Ω_m(1+z)² + Ω_Λ₀
c) H²/H ² = Ω_m(1+z)⁴ + Ω_Λ₀
d) H²/H ² = Ω_m(1+z) + Ω_Λ₀
Answer: a) H²/H ² = Ω_m(1+z)³ + Ω_Λ₀
26. The equation P(k) k^n describes:∝
a) Power spectrum of density fluctuations
b) Pressure of cosmic fluid
c) Potential energy of dark matter
d) Period of cosmic inflation
Answer: a) Power spectrum of density fluctuations
27. The equation ρ_r a ⁴ describes the evolution of:∝ ⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
28. The Sachs-Wolfe effect is described by the equation ΔT/T = -Φ/3, where Φ represents:
a) Gravitational potential
b) Electrostatic potential
c) Scalar field potential
d) Vector potential
Answer: a) Gravitational potential
29. The equation N = ln(a_f/a_i) defines:
a) Number of e-foldings during inflation
b) Number density of galaxies
c) Neutron-to-proton ratio
d) Nucleosynthesis efficiency
Answer: a) Number of e-foldings during inflation
30. The Friedmann equation can be written as Ω_total - 1 = k/(aH)². What does this equation
relate to?
a) Total energy density
b) Spatial curvature
c) Dark energy
d) Inflation
Answer: b) Spatial curvature
31. The equation d_A = d_L/(1+z)² relates:
a) Angular diameter distance and luminosity distance
b) Proper distance and comoving distance
c) Hubble distance and particle horizon
d) Einstein radius and Schwarzschild radius
Answer: a) Angular diameter distance and luminosity distance
32. The Λ equation of state, p = -ρc², corresponds to w = ?
a) 0
b) 1/3
c) -1/3
d) -1
Answer: d) -1
33. The equation ρ_c = 3H²/(8πG) defines:
a) Critical density
b) Dark energy density
c) Matter density
d) Radiation density
Answer: a) Critical density
34. The Hubble time is defined as:
a) t_H = 1/H₀
b) t_H = H₀
c) t_H = 2/H₀
d) t_H = H /2₀
Answer: a) t_H = 1/H₀
35. The equation σ_8 = (δM/M)² ^(1/2) for R = 8h ¹Mpc defines:⟨ ⟩ ⁻
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
36. The equation Ω_k = 1 - Ω_m - Ω_Λ - Ω_r defines:
a) Total density parameter
b) Curvature density parameter
c) Dark energy density parameter
d) Radiation density parameter
Answer: b) Curvature density parameter
37. The equation T 1/a describes the evolution of:∝
a) Cosmic time
b) Temperature of the universe
c) Tension of cosmic strings
d) Tidal forces in galaxies
Answer: b) Temperature of the universe
38. The equation ρ_Λ = Λc²/(8πG) defines:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
39. The equation δ a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: b) Matter-dominated era
40. The equation H(z) = H E(z), where E(z) = [Ω_m(1+z)³ + Ω_r(1+z)⁴ + Ω_k(1+z)² + ₀
Ω_Λ]^(1/2), defines:
a) Hubble parameter as a function of redshift
b) Hubble constant
c) Hubble flow
d) Hubble sphere
Answer: a) Hubble parameter as a function of redshift
41. The equation t a^(3/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: b) Matter-dominated era
42. The equation ρ_m a ³ describes the evolution of:∝ ⁻
a) Radiation density
b) Dark energy density
c) Matter density
d) Curvature density
Answer: c) Matter density
43. The equation d_H = c/H defines:₀
a) Hubble distance
b) Proper distance
c) Comoving distance
d) Angular diameter distance
Answer: a) Hubble distance
44. The equation w = p/(ρc²) defines:
a) Equation of state parameter
b) Dark energy density
c) Matter density
d) Curvature parameter
Answer: a) Equation of state parameter
45. The equation Ω = ρ/ρ_c defines:
a) Hubble parameter
b) Density parameter
c) Deceleration parameter
d) Slow-roll parameter
Answer: b) Density parameter
46. The equation q = -aä/(ȧ)² defines:
a) Charge of the universe
b) Quantum fluctuations
c) Quasar luminosity function
d) Deceleration parameter
Answer: d) Deceleration parameter
47. The equation δT/T ≈ 10 ⁵ describes:⁻
a) Temperature fluctuations in the CMB
b) Time dilation in general relativity
c) Thermodynamic equilibrium in the early universe
d) Tensor perturbations from inflation
Answer: a) Temperature fluctuations in the CMB
48. The equation r = c/(aH) defines:
a) Radius of the observable universe
b) Comoving Hubble radius
c) Relativistic beaming factor
d) Reionization redshift
Answer: b) Comoving Hubble radius
49. The equation N_eff ≈ 3.046 represents:
a) Number of effective neutrino species
b) Neutron-to-proton ratio
c) Normalization of the power spectrum
d) Non-Gaussianity parameter
Answer: a) Number of effective neutrino species
50. The equation f = d(ln δ)/d(ln a) defines:
a) Frequency of gravitational waves
b) Growth rate of structure
c) Fraction of dark matter in galaxies
d) Fine-structure constant
Answer: b) Growth rate of structure
51. The equation Ω_Λ = Λ/(3H²) defines:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
52. The equation r_s = ∫ ^(∞) cs(z)/(H(z)(1+z)) dz defines:₀
a) Schwarzschild radius
b) Sound horizon
c) Silk damping scale
d) Streaming velocity
Answer: b) Sound horizon
53. The equation Ω_m + Ω_Λ + Ω_k = 1 represents:
a) Conservation of energy
b) Flatness condition
c) Friedmann equation
d) Cosmic coincidence
Answer: c) Friedmann equation
54. The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
The equation δ a^(-3/2) describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
55. The equation P(k) = Ak^n T²(k) represents:
a) Primordial power spectrum
b) Pressure of the cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
56. The equation t a^(1/2) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: a) Radiation-dominated era
57. The equation ρ_k = -3kc²/(8πGa²) defines:
a) Kinetic energy density
b) Curvature energy density
c) Dark energy density
d) Radiation energy density
Answer: b) Curvature energy density
58. The equation H² = (8πG/3)ρ - kc²/a² + Λ/3 is known as:
a) Einstein's field equation
b) Friedmann equation
c) Raychaudhuri equation
d) Boltzmann equation
Answer: b) Friedmann equation
59. The equation z_eq = Ω_m/Ω_r - 1 defines:
a) Redshift of reionization
b) Redshift of recombination
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: c) Redshift of matter-radiation equality
60. The equation dn/dln M = (ρ_m/M) f(σ) d ln σ ¹/d ln M represents:⁻
a) Halo mass function
b) Number density of galaxies
c) Dark matter annihilation rate
d) Neutrino mass spectrum
Answer: a) Halo mass function
61. The equation Ω_DE(a) = Ω_DE,0 a^(-3(1+w)) describes the evolution of:
a) Matter density
b) Radiation density
c) Dark energy density
d) Curvature density
Answer: c) Dark energy density
62. The equation d_c = c ∫ ^z dz'/H(z') defines:₀
a) Comoving distance
b) Proper distance
c) Angular diameter distance
d) Luminosity distance
Answer: a) Comoving distance
63. The equation n_s = 1 + 2η - 6ε represents:
a) Number density of stars
b) Neutrino mixing angle
c) Scalar spectral index
d) Dark energy equation of state
Answer: c) Scalar spectral index
64. The equation τ = ∫ n_e σ_T c dt defines:
a) Cosmic time
b) Optical depth
c) Hubble time
d) Recombination time
Answer: b) Optical depth
65. The equation ρ_ϕ = ϕi²/2 + V(ϕ) represents:
a) Radiation energy density
b) Matter energy density
c) Scalar field energy density
d) Dark energy density
Answer: c) Scalar field energy density
66. The equation δT/T = -ϕ/3 - 2v_e·n describes:
a) Sachs-Wolfe effect
b) Sunyaev-Zel'dovich effect
c) Integrated Sachs-Wolfe effect
d) Rees-Sciama effect
Answer: a) Sachs-Wolfe effect
67. The equation f_NL(ϕ_g) = 5/3(ϕ_g - ϕ_g² ) defines:⟨ ⟩
a) Non-Gaussianity parameter
b) Neutrino flavor oscillation
c) Nuclear fusion rate
d) Neutron star equation of state
Answer: a) Non-Gaussianity parameter
68. The equation R_H = c/H defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: a) Hubble radius
69. The equation ξ(r) = (r/r_0)^(-γ) represents:
a) Galaxy correlation function
b) Dark matter density profile
c) Cosmic string tension
d) Inflationary potential
Answer: a) Galaxy correlation function
70. The equation Ω_b h² = 0.02230 ± 0.00014 (68% CL) represents:
a) Total matter density
b) Dark energy density
c) Baryon density
d) Neutrino density
Answer: c) Baryon density
71. The equation t_rec ≈ 380,000 years represents:
a) Age of the universe at recombination
b) Time of galaxy formation
c) Duration of inflation
d) Lifetime of massive stars
Answer: a) Age of the universe at recombination
72. The equation M_J T^(3/2) ρ^(-1/2) defines:∝
a) Jeans mass
b) Solar mass
c) Black hole mass
d) Galaxy cluster mass
Answer: a) Jeans mass
73. The equation r = 2GM/c² defines:
a) Hubble radius
b) Schwarzschild radius
c) Einstein radius
d) Planck length
Answer: b) Schwarzschild radius
74. The equation Ω_k = -k/(a²H²) represents:
a) Matter density parameter
b) Dark energy density parameter
c) Radiation density parameter
d) Curvature density parameter
Answer: d) Curvature density parameter
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
75. The equation dN/dz = 4πc(1+z)²D_A²/(H(z)) defines:
a) Number count of galaxies
b) Neutrino mass spectrum
c) Dark matter annihilation rate
d) Cosmic ray flux
Answer: a) Number count of galaxies
76. The equation T_CMB = T_0 (1+z) describes:
a) Temperature of stars
b) Temperature of the CMB
c) Temperature of the IGM
d) Temperature of dark matter
Answer: b) Temperature of the CMB
77. The equation P_ζ(k) = A_s (k/k_*)^(n_s - 1) represents:
a) Primordial power spectrum
b) Pressure of cosmic fluid
c) Probability of galaxy formation
d) Polarization of the CMB
Answer: a) Primordial power spectrum
78. The equation Ω_r h² = 4.15 × 10 ⁵ represents:⁻
a) Matter density
b) Dark energy density
c) Radiation density
d) Curvature density
Answer: c) Radiation density
79. The equation d_L = (1+z) d_C defines:
a) Luminosity distance
b) Angular diameter distance
c) Proper distance
d) Comoving distance
Answer: a) Luminosity distance
80. The equation σ_8 ≈ 0.8 represents:
a) Matter power spectrum
b) Cosmic microwave background anisotropy
c) Density fluctuation amplitude
d) Galaxy correlation function
Answer: c) Density fluctuation amplitude
81. The equation H_0 = 100h km/s/Mpc defines:
a) Hubble constant
b) Hubble parameter
c) Hubble time
d) Hubble distance
Answer: a) Hubble constant
82. The equation ϕr + 3Hϕi + V'(ϕ) = 0 represents:
a) Friedmann equation
b) Scalar field equation of motion
c) Fluid equation
d) Boltzmann equation
Answer: b) Scalar field equation of motion
83. The equation z_reion ≈ 8 represents:
a) Redshift of recombination
b) Redshift of reionization
c) Redshift of matter-radiation equality
d) Redshift of decoupling
Answer: b) Redshift of reionization
84. The equation f_sky = A_survey / 4π defines:
a) Sky coverage fraction
b) Gravitational lensing efficiency
c) Dark energy equation of state
d) Cosmic variance
Answer: a) Sky coverage fraction
85. The equation Ω_Λ ≈ 0.7 represents:
a) Matter density parameter
b) Radiation density parameter
c) Dark energy density parameter
d) Curvature density parameter
Answer: c) Dark energy density parameter
86. The equation T_0 ≈ 2.725 K represents:
a) Temperature of the Sun
b) Temperature of the CMB today
c) Temperature at recombination
d) Temperature of dark matter
Answer: b) Temperature of the CMB today
87. The equation ρ_crit = 3H²/(8πG) defines:
a) Dark energy density
b) Matter density
c) Critical density
d) Radiation density
Answer: c) Critical density
88. The equation δ ln a describes the growth of density perturbations in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
89. The equation k_eq = H_0 √(2Ω_m) (Ω_r/Ω_m)^(1/2) defines:
a) Wavenumber at matter-radiation equality
b) Curvature of space
c) Kinetic energy of dark matter
d) Konstant of proportionality in Hubble's law
Answer: a) Wavenumber at matter-radiation equality
90. The equation N_ν ≈ 3 represents:
a) Number of inflation fields
b) Number of neutrino species
c) Number of dark matter particles
d) Number of extra dimensions
Answer: b) Number of neutrino species
91. The equation R = 6(ä/a + ȧ²/a²) defines:
a) Ricci scalar
b) Rotation curve
c) Reionization efficiency
d) Relativistic beaming factor
Answer: a) Ricci scalar
92. The equation λ_J = c_s √(π/(Gρ)) defines:
a) Jeans length
b) de Broglie wavelength
c) Compton wavelength
d) Planck length
Answer: a) Jeans length
93. The equation w_0 + w_a(1-a) represents:
a) Equation of state for matter
b) Parameterization of dark energy equation of state
c) Weak lensing efficiency
d) White dwarf mass-radius relation
Answer: b) Parameterization of dark energy equation of state
94. The equation t_U ≈ 13.8 Gyr represents:
a) Time since Big Bang
b) Time of galaxy formation
c) Duration of cosmic inflation
d) Age of the Solar System
Answer: a) Time since Big Bang
95. The equation f_NL ≈ 0.8 ± 5.0 represents:
a) Neutrino flavor mixing
b) Non-Gaussianity parameter
c) Nuclear fusion efficiency
d) Neutron star equation of state
Answer: b) Non-Gaussianity parameter
96. The equation d_A = d_L / (1+z)² relates:
a) Angular diameter distance and luminosity distance
b) Proper distance and comoving distance
c) Hubble distance and particle horizon
d) Einstein radius and Schwarzschild radius
Answer: a) Angular diameter distance and luminosity distance
97. The equation Ω_m ≈ 0.3 represents:
a) Radiation density parameter
b) Dark energy density parameter
c) Matter density parameter
d) Curvature density parameter
Answer: c) Matter density parameter
98. The equation r = c_s t_e defines:
a) Radius of the observable universe
b) Comoving sound horizon
c) Recombination redshift
d) Reionization optical depth
Answer: b) Comoving sound horizon
99. The equation H(z) = H_0 √(Ω_m(1+z)³ + Ω_Λ) represents:
a) Hubble parameter in ΛCDM model
b) Halo mass function
c) Horizon problem solution
d) Holographic dark energy model
Answer: a) Hubble parameter in ΛCDM model
100. The equation t exp(√(Λ/3)t) describes the age of the universe in:∝
a) Radiation-dominated era
b) Matter-dominated era
c) Dark energy-dominated era
d) Inflationary era
Answer: c) Dark energy-dominated era
