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In time different during the first second after Big Bang than it is now? Inflation had a dramatic effect on space, and spacetime is one thing. Was the properties of time affected too? Curved spacetime around black holes cause funny effects for outside observers, infalling objects appear to never reachthe event horizon. The very early universe was even denser. When we talk about the first second, are such effects accounted for?

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Food for thought on density and time dilation. Density isn't gravity. We tend to think it is, but it's not. Variation in density gives us gravity.

If you have an infinite universe, very young, hot and dense, but it's uniform, then you have no time dilation. One way to think about this is to ask if light passing through the universe is red shifted or blue shifted. If the universe is uniform and infinite, it's the same in all directions around the photon, so the photon is neither red nor blue shifted, so, contrary to what our intuition about relativity tells us, there might not have been a great deal of time dilation in the very young universe.

Of-course the ray of light passing through expanding space is enormously red-shifted, but that doesn't affect time dilation. The gravitational red or blue shift in the very young universe might still be close to zero meaning very little time dilation anywhere.

As the early universe grew less uniform then you had time dilation variations in denser parts of the early Universe but with FTL expansion and gravity limited by the speed of light, it's unclear if there ever was massive time dilation in the young universe (at least, unclear to me, if somebody here knows 100%, feel free to post and/or correct me).

Now if we assume the universe is finite and flat and the big bang happened at a point, which, generally isn't the model most people like these days, then you could run into enormous time dilation inside the tiny young and dense universe, but it still expanded FTL, so the calculations get weird and too hard for me. If the expansion of space happens faster than gravity can keep up, gravitational time dilation might not apply, at least not until after the rate of expansion slowed down enough for gravity to permeate the local regions. I couldn't even begin to run the math on this and you'd have different answers for different models too, I'd think. I agree with Andy though, it would need to be accounted for or the models wouldn't be much good.

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Curved spacetime around black holes cause funny effects for outside observers, infalling objects appear to never reachthe event horizon. The very early universe was even denser. When we talk about the first second, are such effects accounted for?

These time dilation effects are (always) accounted for. An observer at any "place" in the inflating universe would experience time at his, her or its own rate. Several observers might find they had experienced different rates of time if they gathered together afterwards and compared notes, however.

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