# 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, 2015 at 21:17

$$\rho_{\text{matter}} = \rho_{\text{matter}}^0(1+z)^3,$$ $$\rho_{\text{radiation}} = \rho_{\text{radiation}}^0(1+z)^4,$$ where $$\rho^0$$ denotes the current enegy density.
This gives us $$z_{eq} = \frac{\rho_{\text{matter}}^0}{\rho_{\text{radiation}}^0} -1 \sim 3400.$$