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**Question:**

Estimate the rate of continuous creation required to keep the density of the universe constant at 10

^{-26}kg/m

^{3}. Express your answer in protons/year/km

^{3}.

**Attempt:**

Assuming a spherical matter-dominated Friedmann universe, we know from solving the fluid equation that ρ ∝ 1/a

^{3}(where ρ is the energy density and

*a*is the scale factor).

I believe the result of the continuous creation is that ∂ρ/∂r = 0 - hence the change in density due to expansion is cancelled out by the change in density due to the continuous creation:

∂ρ

_{expansion}/∂r = -∂ρ

_{creation}/∂r

Thus I am expecting that the continuous creation's energy density will vary as ρ

_{creation}∝ a

^{3}.

However I do not know how to progress this any further, such that any advice, suggestions or solutions would be greatly appreciated! Note: I do not know what the correct answer is!