8.6-7

Question 1

CMB Characteristics

Answer 1

• Isotropic
• Black-Body Radiation
• T_CMB = 2.73 ± 0.06 K

Question 2

Interpretation of CMB

Answer 2

• Redshifted radiation from hot big bang
• Universe expanding and cooling

Question 3

Energy Density of Background Radiation

Answer 3

ρ_Rc² = a_BT⁴, where a_B is the radiation constant

Question 4

Relation Between Energy Density and Scale Factor

for radiation

Answer 4

ρ_R = ρ_R,0 (a₀/a)⁴

Question 5

Temperature Evolution of CMB (proportionality relation)

Answer 5

T_CMB ∝ 1/a

Question 6

Friedmann Equation for Flat Universe

Answer 6

a_dot = a₀²/a √(8πGρ_R,0/3)

i think we can derive this if we just plug in k=0 into the original equation and using the radiation density as a function of a

Question 7

Temperature Evolution of the Early Universe (temperature as a function of time)

Answer 7

• T = (3c²/32πGa_B)¼ t⁻½
• T[K] = 1.52×10¹⁰/√t[s]

Question 8

Hubble Constant

Answer 8

H₀ = 71 km/(s Mpc)

Question 9

Energy Densities in the Universe

Answer 9

• Ω_b ≈ 0.05 (baryonic)
• Ω_d ≈ 0.25 (dark matter)
• Ω_Λ ≈ 0.7 (dark energy)

Question 10

Current Values for Densities (critical and dark)

Answer 10

• Critical density: ρ_c,0 ≈ 1 · 10^-26 kg/m³
• Dark matter density: ρ_d,0 ≈ 2.5 · 10^-27 kg/m³

Question 11

Dark Matter

Answer 11

• Galactic rotation (MW) -> DM in halo
• Mass luminostiy relation of galaxy clusters (mass through virial theorem)
• Gravitational lensing
• Map with CMB