Background Cosmology Flashcards
1
Q
Friedmann equation
A
(a dot / a)^2 = 8 pi G rho/3 - kc^2/a^2
2
Q
H^2/H_0^2=
A
Omega_r(1+z)^4 + Omega_m(1+z)^3+Omega_k*(1+z)^2 + Omega_lambda
3
Q
density with w’s
A
rho = rho_0*a^(-3(1+w))
4
Q
scale factor with w’s
A
a = a_0*t^(2/(3(1+w))
5
Q
w’s
A
rad: 1/3
matter: 0
curvature: -1/3, k=-1
lambda: w=-1
6
Q
Horizon
A
r = integrate from 0 to t over c/a dt
7
Q
Inflation scale factor
A
a ~ exp(t/T)
8
Q
Radiation scale factor
A
a ~t^(1/2)
9
Q
Matter scale factor
A
a ~ t^(2/3)
10
Q
Dark energy scale factor
A
a~exp(t)
11
Q
FLRW metric
A
ds^2=cdt^2 - a^2[dr^2/(1-kr^2)+ r^2(dtheta^2+sin(theta)^2 dphi^2)]
12
Q
density as function of H
A
rho=3H^2/(8piG) = 1/(6pi(1+w)^2 G t^2)
13
Q
Horizon as function of z
A
r = integrate from 0 to z over c/H dz
14
Q
Luminosity distance in flat universe
A
d_L=r(1+z)
15
Q
Angular distance in flat universe
A
d_A = r/(1+z)
