Question

What formula is used to calculate the age of the universe?

Answer 1

Use Hubble constant relationship to time, i.e.:

`t = 1/H_o`

substitute an estimate for Hubble constant `75 (km)/s/(Mpc)`, and knowing that `=>1Mpc= 3.09xx10^19 km`

`t = 1/(75(km)/s)*(3.09xx10^19 km)=4.12xx10^17 s`

convert to years

`t = 4.12xx10^17 s * 1/60min/s*1/60(hr)/min*1/24 (day)/(hr)*1/365(yrs)/(day)`

`t= 1.308xx10^10`

but be carefully there are 5 cases:

1) Non-zero cosmological Constant (yes that Einstein cosmos constant): `t > 1/H_o`
2) Empty Universe model (no mass): `t = 1/H_o`
3) Open: `t ge 1/H_o > 2/3H_o`
4) If the universe has exactly the right amount of mass, it will neither stop expanding, nor re-contract either. This model is referred to as the “critical universe”: `t =2/3 1/H_o`
5) Open Model: `t < 2/3 1/H_o`

Typically what you will hear is the universe is 13.8 billion years old, that is `13.8xx10^9` clearly this tends to Empty or Non-zero cosmological Constant Universe.