The Big Bang Theory's description of the universe relies on reliable physics up to which theoretical time limit?

Answer

The Planck epoch ($10^{-43}$ seconds)

Physics breaks down before the Planck epoch ($10^{-43}$ seconds) because the extreme conditions require a successful theory of Quantum Gravity, which currently does not exist.

The Big Bang Theory's description of the universe relies on reliable physics up to which theoretical time limit?
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