CosmoCard

Steinhardt, 2007

Einstein Eq.: $H^2 =\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho-
\frac{k}{a^2}; k=(+1, 0,  -1)= ({\rm closed}, {\rm flat}, {\rm open})$
Equation-of-state $w \equiv p/\rho$: $\rho \sim a^{-3(1+w)}$; $a \sim t^{2/[3(1+w)]}$

Hubble constant $= H_0= 71.0 \pm 2.6$ km sec$^{-1}$ Mpc$^{-1}$ or $h=0.710 \pm 0.0026$
1 km/s $= 0.98$ pc/Myr $ \approx 10^{-12}$ Mpc/yr
Hubble time $= H_0^{-1}= 3.086 \times 10^{17} h^{-1}  {\rm sec}$ $= 9.778
\,h^{-1}\, {\rm Gyr}= 4.35 \times 10^{17} \,{\rm sec} $
Hubble distance $c H_0^{-1} = 2997.9   h^{-1}$ Mpc $= 9.2503 \times 10^{27}
h^{-1}$ cm
Age of the Universe $= 13.77 \pm 0.15 {\rm Gyr}$
$\Omega_b=0.044$ $\Omega_{DM} = 0.221$ $\Omega_m=0.265 $ $\Omega_{\Lambda}=0.735$ $\pm 0.030$
$\Omega_b h^2 = 0.0223 \pm 0.0007$ $\Omega_m h^2 = 0.133 \pm 0.006$
$\rho_{DM}=1.17 \times 10^{-6}$ GeV/cm$^3$ (but $0.4$ GeV/cm$^3$ near sun)
$q_0 = - \frac{\ddot{a} a}{\dot{a}^2} = \frac{\Omega_m}{2} - \Omega_{\Lambda}
+ \frac{1}{2}(1+3 \gamma) \Omega_{\gamma}$
Luminosity distance: $d= H_0^{-1} [ z + \frac{1}{2}(1-q_0) z^2 + \ldots] $
Angular distance = (Luminosity distance)$/(1+z)^2$
BH Lifetime= $2 \times 10^{67}(M/ M_{\rm solar})^3$ yr

Critical Density ($\Omega_m=1$): $= 8.0992 h^2 \times 10^{-47}$ GeV$^{-4}$ $=
1.8791 h^2 \times 10^{-29}$ g cm$^{-3}$
Fluct. amp. $\Delta_{\cal R}^2$ ($k=0.002$/Mpc) $= 24.1 \pm 1.3 \times 10^{-10}$

Cosmic Microwave Background: $T= 2.725 \pm 0.002$ K
Cosmic Neutrino Background: $T= 1.945 \pm .003$ K
Matter-Radiation Equality: $a_{eq}=4.1707 \times 10^{-5}   (\Omega_m h^2)^{-1} a_0$ $T_{eq} = 5.6362  (\Omega_m h^2)$ eV
Planck Mass($M_P$) $=(1/G)^{1/2} = 1.2211 \times 10^{19}$ GeV or "reduced $M_p$" $=2.4 \times 10^{18}$ GeV
1 Mpc $= 3.085 \times 10^{24}$ cm= $1.5637 \times 10^{38}$ GeV$^{-1}$= $
3.2615 \times 10^6$ l-yr
1 GeV $=1.1605 \times 10^{13}$ K $=1.6022 \times 10^{-3}$ erg $= 5.0676 \times
10^{13}$ cm $^{-1} = 1.5192 \times 10^{24}$ sec$^{-1}$
1 GeV $^{3}= 1.3014 \times 10^{41}$ cm$^{-3}$ 1 GeV $^{4}=
2.3201 \times 10^{17}$ g cm$^{-3}$
$M_{\rm solar} = 1.99 10^{33}$ g $= 1.116 \times 10^{57}$ GeV



Paul Steinhardt 2007-05-24