# Redshift of mass-dominant universe

What was the value of redshift $z$ when matter started to dominate the universe?

Is there any way to calculate it without knowing the time?

• $z_{eq} \sim 3000$. It should be easy to calculate if you know the present amount of radiation and matter energy density. – Ihle Nov 1 '15 at 21:17

We can calculate the redshift of matter-radiation equality by using the scaling of the energy density of radiation and matter:

$$\rho_{matter} = \rho_{matter}^0(1+z)^3,$$ $$\rho_{radiation} = \rho_{radiation}^0(1+z)^4,$$ where $\rho^0$ denotes the current enegy density.

This gives us $$z_{eq} = \frac{\rho_{matter}^0}{\rho_{radiation}^0} -1 \sim 3400.$$

The exact current value can be found in: http://planck.caltech.edu/pub/2015results/Planck_2015_Results_XIII_Cosmological_Parameters.pdf