Question

What will the Hubble parameter be 10 billion years from now for (a) a universe with H_0 = 70 km/sec/Mpc, and critical density in matter and (b) the Universe we think we live in, which has matter density of about 0.3 of critical density, and cosmological constant of 0.7 of critical density, and a Hubble constant of 70 km/sec/Mpc?

Answer 1

The Hubble time is given by, t_H = 1 / H₀

where, H₀ = Hubble constant = 70 km/sec/Mpc

then, we get

t_H = 1 / ( 70 km/sec/Mpc) = 4.408 x 10¹⁷ sec

converting sec into billion years -

t_H = 13.9 billion years

(a) The Hubble parameters for a universe will be given as :

using a formula, we have

H = $\dot{a}$ / a = constant $\Rightarrow$ a $\propto$ e^Ht = e^t/t_H

H = e^t/t_H = e^(10/13.9)

H = 2.05