# Astronomy coursework question

## Homework Statement

Assume that the vast majority of the photons in the present Universe are cosmic microwave radiation photons that are a relic of the big bang. For simplicity, also assume that all the photons have the energy corresponding to the wavelength of the peak of a 2.73K black-body radiation curve. At Approximately what redshift will the energy density in radiation be equal to the energy density in matter?

(hint: work out the energy density in photons at the present time. Then work it out for baryons, assuming a proton for a typical baryon. Remember how the two quantities scale with redshift to work out when the energy density is the same.)

## Homework Equations

$$\rho_M \propto a^{-3}$$

$$\rho_\gamma \propto a^{-4}$$

$$T \propto a^{-1}$$

$$1 + z = \frac{v}{v_0} = \frac{\lambda_0}{\lambda} = \frac{a(t_0)}{a(t)}$$

## The Attempt at a Solution

Not sure where to start.. how do I work out the energy density for photons and protons at the present time? Do I use E = mc^2?