Quiz Flashcards
(30 cards)
What is the Friedmann equation and what does each term represent?
H^2 = (8πG/3)ρ - K/R^2; relates expansion to energy density and curvature
Define critical density and its importance.
ρ_c = 3H^2 / 8πG; density needed for a flat universe
What is the density parameter Omega?
Ω = ρ / ρ_c; tells if universe is open, flat or closed
How does the redshift relate to scale factor?
1 + z = R_0 / R(t)
What does g_* represent?
Effective relativistic degrees of freedom for energy density
How does the energy density scale with temperature?
ρ ∝ g_* T^4
What is the entropy density formula?
s = (2π^2 / 45) g_*s T^3
What condition defines freeze-out?
Γ ≈ H, where interaction rate falls below expansion rate
How do you estimate relic abundance?
Ωχ h^2 ≈ 3 × 10^{-27} / <σv></σv>
What is the equilibrium number density of non-relativistic particles?
n_eq ∝ e^{-m/T}
Describe neutrino flavor mixing.
|ν_α⟩ = Σ U_αi |ν_i⟩
What is the oscillation probability formula?
P(ν_e → ν_μ) = sin²(2θ) sin²(Δm²L/4E)
What is the significance of MSW effect?
Matter-enhanced neutrino oscillation
What is the neutron-proton ratio at BBN freeze-out?
n/p ≈ e^{-Δm/T} ≈ 1/6
What is the expected helium mass fraction from BBN?
Y_p ≈ 0.25
What does the CMB power spectrum tell us?
Information about geometry, baryon content, and perturbations
What is C_ℓ in the CMB context?
C_ℓ = ⟨|a_ℓm|²⟩, power in angular mode ℓ
What is the matter power spectrum?
P(k) = ⟨|δ_k|²⟩, shows amplitude of density perturbations at scale k
How does δ grow in matter domination?
δ ∝ R(t)
What are the Sakharov conditions?
B violation, C/CP violation, out of equilibrium
What is the GUT running coupling formula?
1/α_i(μ) = 1/α_i(M_Z) + b_i/2π ln(μ/M_Z)
What process demonstrates GUT-scale baryon violation?
p → e⁺ + π⁰
What kind of particle is an axion?
Light pseudoscalar, dark matter candidate from strong CP problem
What’s the typical freeze-out temperature for a WIMP?
T_f ≈ m_χ / 25
