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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?

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

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