That is the idea behind Conformal Cyclic Cosmology, hypothesized by the titanic Roger Penrose. [1] However, he has considered a couple different possibilities:

That is the idea behind Conformal Cyclic Cosmology, hypothesized by the titanic Roger Penrose. [1] However, he has considered a couple different possibilities: [Possibility 1] The last eon's heat death determines the big bang's character which in turn determines the distribution of matter-energy in the universe, ie. cosmic microwave background distribution [Possibility 2] There is no information able to pass from universe to universe, ie. the state of the big bang is essentially {}, a null state. Any asymmetry in the big bang is due to purely JIT QM. Nonetheless, the crux of the theory is that a heat death is the conformal equivalent of a big bang, since there are no particles with mass, thus no clocks/time. [1] https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology