Calculate Time Dilation b/w t1 & t2 Using Average Mean Density

[Ans]

I thinking how to calculate time dilation in different time with usage of average mean density.
Lets set that Universe have average mean density $\Omega_{t1}$ at time t1 and $\Omega_{t2}$ at time t2.
How to get time dilation, for comoving observers, between time t1 and t2?

 

[mfb]

Time dilation of what relative to what?

 

[Ans]

Time dilation of what relative to what?

Dilation of time if Universe had density $\Omega_{t1}$ to case if Universe had density $\Omega_{t2}$ and same size.

 

[mfb]

Time dilation is something one reference frame has relative to the other in the same universe. Using it as absolute value does not make sense.

 

[russ_watters]

First of all, this is a Relativity question, so I'm moving this to the Relativity section.

Have you looked-up the equation for gravitational time dilation? Do you understand, in general, how to use it?

What you are describing (using mass density) isn't a common case of how the equation is used, but you may be able to utilize it for a similar purpose. One thing you will notice about the equation though, is that when you are far away from a massive object, it returns the result t₀=t_f (no time dilation). Depending on the particular thing you are trying to find, the answer may simply be that there is no significant time dilation due to the density of the universe.

 

[russ_watters]

Time dilation is something one reference frame has relative to the other in the same universe. Using it as absolute value does not make sense.

While it doesn't make sense to talk about different universes, it wouldn't be fundamentally different for the OP's problem to talk about different places in the current universe that have different densities...

...the issue I see is how to apply density to the equation at all.

 

[Finny]

"How to get time dilation, for comoving observers, between time t1 and t2?"

If I understand your question correctly, I think the answer you seek is that there is no time dilation for co moving observers. Time has passed at a fixed rate for co moving observers for the duration of the universe.

Such observers agree with one another on the amount of clock time since the Big Bang, and this is what we mean when we speak of the age of the universe in the FLRW cosmological model...13.8B years as the age of the universe.

 

[Ans]

Have you looked-up the equation for gravitational time dilation? Do you understand, in general, how to use it?
.

I think yes, at least I studied GR in university some years ago. But I work in area not related to GR.
Problem is - I have some new hypothesis not related to cosmology, and unexpectedly found it is necessary to test the hypothesis with cosmology models.
Well, I think I got some ideas for my tests, thanks.

 

[PeterDonis]

Have you looked-up the equation for gravitational time dilation?

This won't help, because gravitational time dilation is only meaningful in stationary spacetimes, and the spacetime of the universe is not stationary (because the universe is expanding).

 

[Chalnoth]

I thinking how to calculate time dilation in different time with usage of average mean density.
Lets set that Universe have average mean density $\Omega_{t1}$ at time t1 and $\Omega_{t2}$ at time t2.
How to get time dilation, for comoving observers, between time t1 and t2?

There's no time dilation as a result of the average density of the universe.