This is a simple cosmology calculator. It can be used to compute the age of the universe for a given set of parameters, as well as the comoving distance and light travel time for a given redshift.

Parameter Symbol Value Unit
Hubble constant H0 km/s/Mpc
Matter density Ωm
Dark energy density ΩΛ
—  Spatial curvature Ωk
Age of the universe t0   Gyr

Redshift z
Age at redshift t   Gyr
Light travel time     Gyr
Comoving distance d   Mpc

The age of the universe at redshift $z$ is calculated using [1]:

$$t(z)=\frac{1}{H_0}\int_0^{1/(1+z)}\frac{dx}{x\sqrt{\Omega_\Lambda+\Omega_kx^2+\Omega_mx^3}}.$$

The comoving distance, in turn, is calculated as

$$d(z)=\frac{c}{H_0}\int_0^z\frac{dx}{\sqrt{\Omega_\Lambda+\Omega_k(1+x)^2+\Omega_m(1+x)^3}}.$$

In all these calculations, we assume $\Omega_\gamma=0$, i.e., the density parameter for radiation is assumed to be negligible.

Results may differ from those calculated using other cosmology calculators because of different rounding (in numerical integration, in particular) and, well, because this one is brand spanking new and may have bugs!

[1] Weinberg, S: Cosmology, Oxford U. Press (2008)