For a Hubble constant

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Cosmological models, parameters and the dark sector · Cosmological models, parameters and the dark sector

The Geometry of Gravity, Ch FRW cosmology as an exact solution

Problem

For a Hubble constant H0=70.0 km s−1Mpc−1H_0 = 70.0\ \text{km s}^{-1}\text{Mpc}^{-1}, compute: ((a)) the critical mass density ρcrit/c2=3H02/(8πG)\rho_{\rm crit}/c^2 = 3H_0^2/(8\pi G), in kg m−3^{-3}; ((b)) the Hubble time 1/H01/H_0, in gigayears (1 Gyr =3.156×1016=3.156\times10^{16} s). Use G=6.674×10−11 N m2kg−2G = 6.674\times10^{-11}\ \text{N m}^2\text{kg}^{-2} and 1 Mpc=3.086×1022 m1\ \text{Mpc} = 3.086\times10^{22}\ \text{m}.

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