I How to calculate the mass within the Hubble Sphere?

  • I
  • Thread starter Thread starter timmdeeg
  • Start date Start date
AI Thread Summary
To calculate the mass within the Hubble Sphere using the L-CDM model, one can determine the average density and multiply it by the Hubble volume. The density is approximated as critical density, given by the formula ρ = 3H² / (8πG). The Hubble volume is calculated as 4πc³ / (3H³), leading to the mass of the Hubble volume being expressed as c³ / (2HG). Notably, this mass decreases in proportion to the Hubble parameter, indicating that as the Hubble parameter decreases, the mass of the Hubble volume increases. This relationship highlights the dynamic nature of mass within the expanding universe.
timmdeeg
Gold Member
Messages
1,538
Reaction score
342
How to calculate the mass within the Hubble Sphere and its time dependence, assuming the L-CDM model?
 
Space news on Phys.org
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.
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
The formal paper is here. The Rutgers University news has published a story about an image being closely examined at their New Brunswick campus. Here is an excerpt: Computer modeling of the gravitational lens by Keeton and Eid showed that the four visible foreground galaxies causing the gravitational bending couldn’t explain the details of the five-image pattern. Only with the addition of a large, invisible mass, in this case, a dark matter halo, could the model match the observations...
Hi, I’m pretty new to cosmology and I’m trying to get my head around the Big Bang and the potential infinite extent of the universe as a whole. There’s lots of misleading info out there but this forum and a few others have helped me and I just wanted to check I have the right idea. The Big Bang was the creation of space and time. At this instant t=0 space was infinite in size but the scale factor was zero. I’m picturing it (hopefully correctly) like an excel spreadsheet with infinite...
Back
Top