Calculating Universe Density: Cosmology Equations

[AleksanderPhy]

Hello I have question about universe density so is there any equation what says how to calculate universe density because on meany cosmology equations.

 

[mfb]

Calculate it based on what?
You need some measurement input.

 

[ayush solanki]

First of all we don't have any absolute or right idea how big our universe is. And also the universe is expanding.so the volume of the universe is not absolute.even if you use the general formula of density:-

Density=mass/volume
Than too you will need mass and the volume of the universe,which I don't think you can do.yet.

 

[mfb]

You don't have to know the overall size of the universe to measure its density. You can measure the density of the universe everywhere in the observable part. It is extremely uniform (if we account for expansion over time). It is reasonable to assume that it doesn't change significantly outside, but usually statements are made about the observable part only.

 

[ayush solanki]

Ok thank you

 

[AleksanderPhy]

Thanks(;

 

[marcus]

One way to estimate the density is like this:

It can be determined that the U is spatially flat or else very nearly so. Basically this is done by measuring the angular size of things of known width at known distance. It is involved and it is not perfect. Or one can measure the rate that volume of sphere increases with radius, by galaxy count. All the evidence is consistent with near spatial flatness.

Once that is done then we can apply the Friedmann equation (a simplified version of basic GR equation) for the spatial flat case, and find the density.

A form of the Friedmann equation is this:

H² - H_∞² = (8πG/3)ρ

where rho ρ is the mass density and H is the Hubble constant and H_∞ is the long-term asymptotic value of the Hubble constant to which the present value is seen to be tending.

Aleksander, I think it is very interesting that the Hubble constant (think of it as a percentage growth rate of distances) is not constant over time. Since we can look back in time we can get an idea of how the percentage growth rate is changing! It is declining slowly but the decline is leveling off. The fact that the decline is leveling off at a positive value (not just going to zero) was discovered in 1998.

Einstein included that possibility in the original 1917 GR equation but for most of the time people did not consider it as a serious possibility.

As a percentage growth rate the current H is now about 1/144 of a percent per million years. The longterm growth rate H_∞ that it is tending towards is around 1/173% or 1/174% per million years.

You can calculate the density yourself if you want, by squaring these growth rates, taking the difference, and dividing by (8πG/3), G is just Newton G.

The fact that the H decline is leveling out at a positive constant rate means that the growth of an invidual distance is almost exponential. If the rate were constant it would be exponential at a fixed percentage rate, and it is nearly that. So that is the "acceleration" that people make so much fuss about. It is a very slight acceleration you would see if you watch an individual distance over a long period of time. It just means the decline in H is slowing, H is leveling out at a positive value.

 

[AleksanderPhy]

Thank you for a very enormous article for me It wrealy helped me