GR & Early Universe: Time Dilation & Light Speed

[Juan Carlos del Rio]

TL;DR Summary

According to GR the proper time measured by an observer in a gravity field runs slower compare to another frame with no or less gravity intensity. Looking for relative implications when comparing physical phenomena in different frames with different gravity fields strength

If in the early Universe the matter density was density so large causing an intense gravity field, was the time at that epoch running much more slowly compared to the actual time according to the GR?
If so then, would any reference frame in the early Universe see the light apparently traveling faster than we measure it nowadays? What would the implications be in this case?

 

[Vanadium 50]

More slowly than what? Explain how you would compare two clocks at different times.

 

[Juan Carlos del Rio]

Translating time into space. We should just look into distant stars, galaxies, CMB, etc. I guess that in this case the light received is reddened due to the Universe expansion but could it also be any time dilation factor in this reddening? Or this is just two sides of the same coin? I mean we can see the reddening as space expansion OR time dilation but never with AND

 

[PeterDonis]

According to GR the proper time measured by an observer in a gravity field runs slower compare to another frame with no or less gravity intensity.

These statements have a very important qualifier attached to them: they only apply to a system which is stationary, i.e., whose global properties do not change with time. Only in such systems can the concept of "gravity field" even be defined.

If in the early Universe the matter density was density so large causing an intense gravity field

This is not correct, because the universe is not stationary; it is expanding. That means the concept of "gravity field" can't even be defined for the universe as a whole.

was the time at that epoch running much more slowly compared to the actual time

There is no such thing as "the actual time". Time is not absolute. It's relative. The only invariants are the elapsed time for particular observers between particular events.

 

[PeterDonis]

We should just look into distant stars, galaxies, CMB, etc. I guess that in this case the light received is reddened due to the Universe expansion but could it also be any time dilation factor in this reddening?

There is no way to even define a "time dilation factor" for this case.

 

[Nugatory]

According to GR the proper time measured by an observer in a gravity field runs slower compare to another frame with no or less gravity intensity.

That's not right, although it is a very common misunderstanding. It's not the intensity of the gravitational field that matters, it's the the difference in gravitational potential between the the two observers. Consider for example two observers, one inside of a hollow sphere of matter and the other somewhere outside the sphere. The gravitational field inside the sphere will be zero - no intensity at all - while the observer outside the sphere will be subject to a gravitational field that depends on the mass of the sphere and the distance from it but which will always be greater than zero. However, it's the inside observer whose time will run slower.

Note that this hypothetical hollow sphere is a stationary system. If it weren't, there would be no way of defining the potential and as @PeterDonis says above, no sensible definition of "gravity field"