# Rate of continuous creation

1. May 2, 2016

### epsilon

• Thread moved from the technical forums, so no HH Template is shown.
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 cancelled 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!

2. May 2, 2016

### Simon Bridge

You need to know how the scale parameter $a$ changes with time.

3. May 3, 2016

### epsilon

And so this is the Hubble parameter then?

H = 1/a × da/dt

4. May 3, 2016

### Simon Bridge

That seems a reasonable place to go... a lot depends on your coursework to date.

5. May 4, 2016

### epsilon

OK thank you! :-)