To a first order approximation (e.g. in the FLRW perfect fluid model), a Big Crunch would resemble a time-reversal of the standard big bang cosmology.
In our universe, time reversal results in galaxies appearing at a comoving observer's horizon, and everything inside the horizon becoming denser and hotter.
Ultimately the density and heat is expected to result in beyond-the-Standard Model physics in the matter sector, and (hopefully) new physics in the gravitational sector.
We don't really know what those physics will be. Everyone hopes for something that prevents a gravitational singularity from forming, but so far what we have in terms of possible stabilizers are conjectural at best.
The time-reversals of Big Crunch and the usual-forward-time big bang cosmology with structure formation relate to the BH information loss problem. For a non-eternal BH when we time-reverse from i+ we have a gas of Hawking radiation that collapses into a time-reversed BH which eventually emits matter with much less (Boltzmann) entropy -- ions, molecules, dust, stars and even the things orbiting them. (A time-reversed stellar BH likewise will eventually spit out a white dwarf or neutron star with their respective complex layerings). How does a time-reversed BH "know" how to spit out whole stellar-mass objects when only time-reversed Hawking radiation fell into it? Most quantum gravity programmes hope that strong gravity[1] produces an environment where this sort of (time-reversed) structure formation is likely.
Flipping the arrow(s)-of-time is extremely useful for reasoning in a setting in which strong gravity is important, and extra-underlines the question of why we have the arrow(s)-of-time we do in the first place. "Boundary conditions did it" is pretty unsatisfying.
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[1] i.e., where the radius of curvature is on the order of the Planck length; this mostly comes from the non-renormalizability of perturbatively quantized gravity (where we quantize perturbations of a background metric) and from work in finding the effective field theory limit of semiclassical gravity; generally it's very close to a gravitational singularity and -- depending on the censorship conjecture -- always invisible to outside observers.
To a first order approximation (e.g. in the FLRW perfect fluid model), a Big Crunch would resemble a time-reversal of the standard big bang cosmology.
In our universe, time reversal results in galaxies appearing at a comoving observer's horizon, and everything inside the horizon becoming denser and hotter.
Ultimately the density and heat is expected to result in beyond-the-Standard Model physics in the matter sector, and (hopefully) new physics in the gravitational sector.
We don't really know what those physics will be. Everyone hopes for something that prevents a gravitational singularity from forming, but so far what we have in terms of possible stabilizers are conjectural at best.
The time-reversals of Big Crunch and the usual-forward-time big bang cosmology with structure formation relate to the BH information loss problem. For a non-eternal BH when we time-reverse from i+ we have a gas of Hawking radiation that collapses into a time-reversed BH which eventually emits matter with much less (Boltzmann) entropy -- ions, molecules, dust, stars and even the things orbiting them. (A time-reversed stellar BH likewise will eventually spit out a white dwarf or neutron star with their respective complex layerings). How does a time-reversed BH "know" how to spit out whole stellar-mass objects when only time-reversed Hawking radiation fell into it? Most quantum gravity programmes hope that strong gravity[1] produces an environment where this sort of (time-reversed) structure formation is likely.
Flipping the arrow(s)-of-time is extremely useful for reasoning in a setting in which strong gravity is important, and extra-underlines the question of why we have the arrow(s)-of-time we do in the first place. "Boundary conditions did it" is pretty unsatisfying.
- --
[1] i.e., where the radius of curvature is on the order of the Planck length; this mostly comes from the non-renormalizability of perturbatively quantized gravity (where we quantize perturbations of a background metric) and from work in finding the effective field theory limit of semiclassical gravity; generally it's very close to a gravitational singularity and -- depending on the censorship conjecture -- always invisible to outside observers.