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After the Big Bang all of the matter in the observable universe was condensed into a space that was very small (grain of rice sized).

The time dilation due to gravity should have been very large. So I’m wondering how long relative to a proper clock the first second of the universe would have taken?

I think I’m supposed to use the Schwarzschild metric for this but I’m not sure I’m applying it the right way.

Thanks

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    $\begingroup$ Actually, the Schwarzschild metric is not the right metric to use here. A family of metrics called FLRW metrics is more appropriate. These metrics describe various versions of an expanding universe. This doesn't answer your question, but it might help put the question in a better context. $\endgroup$ – Dan Yand Dec 23 '18 at 22:46
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The metric appropriate whith an expanding universe is the flrw metric as mentioned by Dan.

How long was the first second? Well...ONE second. When you say that in the region of a strong gravitation force time goes slower, it is because you are comparing it with a region of lower gravity. But in the early universe there was no region of lower gravity since the universe was homogeneous, so there is no way to compare it to something else

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  • $\begingroup$ Thanks. I understand the universe is homogeneous and so 1s would be the same in all reference frames within the universe. The question is relative to t0 or a clock an infinite distance from a gravitational frame. $\endgroup$ – Kyle Dec 24 '18 at 2:11
  • $\begingroup$ @Kyle: It sounds like you are asking about a clock that is outside the universe somehow. How do you think that would be possible? $\endgroup$ – D. Halsey Dec 24 '18 at 16:08
  • $\begingroup$ Aren’t all proper clocks (those an infinite distance away from gravity) outside of the universe? I’m asking just because the difference between proper clock time and the first second must have been huge. So if there are processes that operate under proper clock time and not relative time would have been that much bigger in the early universe. $\endgroup$ – Kyle Dec 24 '18 at 23:09
  • $\begingroup$ No @Kyle I think you got it all wrong. Proper time is the time measured by a free-falling clock. That's it! Forget all about infinite distant clocks residing outside of the universe $\endgroup$ – magma Dec 25 '18 at 0:21
  • $\begingroup$ Thanks @magma. I thought I might be using the term incorrectly that’s why I included the caveat about being outside of the effects of gravitational time dilation. What I’m asking about is relative to a clock with no dilation caused by mass as viewed by the Schwartzchild metric or the equivalent concept in whatever appropriate framework would exist. It seems that there must be one because if matter dilates time now it must also have distorted time during the Big Bang. $\endgroup$ – Kyle Dec 25 '18 at 0:33

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