I How to calculate the mass within the Hubble Sphere?

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How to calculate the mass within the Hubble Sphere and its time dependence, assuming the L-CDM model?
 
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Calculate the average density, multiply by the volume. I think most of that can be got out of Jorrie's calcuator.
 
The density of the universe is very close to the critical density, that is, we can consider it to be ##\rho=\frac {3H^2}{8\pi G}##. On the other hand, the Hubble radius is ##c/H## so the Hubble volume is ##\frac{4\pi c^3}{3H^3}##. The mass of the Hubble volume is density times volume ##\frac {3H^2}{8\pi G}\frac{4\pi c^3}{3H^3}=\frac{ c^3 H}{2G}##. From the above it follows that the mass of the Hubble volume decreases in proportion to the Hubble parameter.

Edit:
The mass of the Hubble volume is density times volume ##\frac {3H^2}{8\pi G}\frac{4\pi c^3}{3H^3}=\frac{ c^3 }{2HG}##.
From the above it follows that the mass of the Hubble volume grows in proportion to how the Hubble parameter decreases
 
Last edited:
Jaime Rudas said:
The mass of the Hubble volume is density times volume ##\frac {3H^2}{8\pi G}\frac{4\pi c^3}{3H^3}=\frac{ c^3 }{2HG}##.
From the above it follows that the mass of the Hubble volume grows in proportion to how the Hubble parameter decreases
Thanks for clarifying.
 
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