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?

  • $\begingroup$ $z_{eq} \sim 3000$. It should be easy to calculate if you know the present amount of radiation and matter energy density. $\endgroup$
    – Ihle
    Nov 1, 2015 at 21:17

1 Answer 1


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

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

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

The exact current value can be found in Page 16, Planck 2018 results. VI. Cosmological parameters.


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