Undergrad How to calculate the mass within the Hubble Sphere?

[timmdeeg]

How to calculate the mass within the Hubble Sphere and its time dependence, assuming the L-CDM model?

 

[Ibix]

Calculate the average density, multiply by the volume. I think most of that can be got out of Jorrie's calcuator.

 

[Jaime Rudas]

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

 

[timmdeeg]

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.