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I just recently found out that one could find the Friedman's equation in Newton's approximation (without GR) by assuming that the universe in homogeneous and isotropic simply by using F=ma and the conservation of energy.

On can then find that the scale factor goes as t^2/3, as expected for a matter dominated universe.

I am trying to do the same thing for a universe dominated by radiation.

The energy inside a box filed with radiation would be ##E=h/\lambda\sim h/R## where ##R## is the scale factor. The energy density would be ##\rho=E/V\sim E/R^3 \sim h/R^4##. One can see the extra dilution factor 1/R when dealing with radiation. If this expression for ##\rho \sim 1/R^4## is put in the Friedman's equation we find ##R\sim t^{1/2}##, as expected for a radiation dominated universe.

What I would like to do is to find the Frieman's equations using Newton and this idea (##E_{rad}\sim 1/R^4##). I But I cannot workout the conservation of the energy nor the Newton's equation F=ma.

Would anyone have a lead ?

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# Radiation dominated universe in Newton's approximation (no )

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