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Question:
Estimate the rate of continuous creation required to keep the density of the universe constant at 10-26kg/m3. Express your answer in protons/year/km3.
Attempt:
Assuming a spherical matter-dominated Friedmann universe, we know from solving the fluid equation that ρ ∝ 1/a3 (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 canceled out by the change in density due to the continuous creation:
∂ρexpansion/∂r = -∂ρcreation/∂r
Thus I am expecting that the continuous creation's energy density will vary as ρcreation ∝ a3.
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!
Estimate the rate of continuous creation required to keep the density of the universe constant at 10-26kg/m3. Express your answer in protons/year/km3.
Attempt:
Assuming a spherical matter-dominated Friedmann universe, we know from solving the fluid equation that ρ ∝ 1/a3 (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 canceled out by the change in density due to the continuous creation:
∂ρexpansion/∂r = -∂ρcreation/∂r
Thus I am expecting that the continuous creation's energy density will vary as ρcreation ∝ a3.
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!