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The traditional view holds that both space and time emerged together from the Big Bang. However, I'm curious about the possibility that time could be eternal, with no beginning, while space began to expand since the singularity of the Big Bang.

According to the Big Bang theory, space and time (spacetime) began approximately 13.8 billion years ago from a singularity.

What if time is eternal, extending infinitely into the past, and only space as we know it emerged at a certain point in time, leading to the observed expansion of the universe?

Theoretical Basis: Is there any theoretical framework or model in cosmology that supports the decoupling of space and time, with time being eternal and space having a finite beginning?

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We really don't know anything about space or time before the Big Bang - or even if the phrase "before the Big Bang" is at all meaningful. This is because General Relativity predicts a singularity in spacetime at the Big Bang. We strongly suspect this cannot be the whole story because a singularity does not really make physical sense. But to extend our models beyond the Big Bang we need (at least) to combine General Relativity and quantum mechanics in a theory of quantum gravity, which we don't have at the moment.

Of course, that doesn't prevent cosmologists, physicists and mathematicians from speculating about cosmological models that include infinite time, multiple Big Bangs etc. - one example is Roger Penrose's conformal cyclic cosmology model.

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As pointed by gandalf61, all we can do here is mostly speculation. We are far from getting answers to these questions, both from theory and observation. I don't know any theoretical framework which would do such a thing.

Now the first question you should ask yourself is whether or not decoupling space and time makes any sense and if it can be motivated any how. What would be an eternal time alone without any space? Even within GR it is not so obvious to separate both. It would basically mean space-time goes suddenly from 1D to 4D. Then why would space start suddenly at primordial singularity? What would trigger this change? Then why would you want time to be eternal and not space and not the other way around?

Those questions are definitely hill defined within our current physics and belong to philosophy (even though there is of course no clear distinction between the two disciplines).

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