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Hi,

I want to obtain a constant that proportional to total matter density of universe.

Let ρ be matter densitiy and ρr be radiation desity.

In an expanding universe volume times total density must be constant. It is wrong?

let me show it is not correct because,

a^3(ρ + ρr) = ρ0 + ρr0/a

where ρ0 is matter density at present and similarly ρr0 is radiation density at present.And "a" is scale factor that function of time coordinate.

As you can see volume times total matter density not constant.

And energy of radiation decays like 1/a due to the expansion, total energy is conserved but energy of radition is not conserved. How this energy transform?

thanks.

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# Finding a constant in an expanding universe

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