The Big Bounce is an alternative to the Big Bang singularity: instead of the universe beginning from an infinitely dense point, a contracting universe bounces and starts expanding. The singularity is avoided. But mathematically, there are two ways to bounce.
Lo Franco and Montani formulate the Quantum Big Bounce for a closed, isotropic universe with an ekpyrotic potential by treating the Wheeler-DeWitt equation as a scattering problem — analogous to the Klein-Gordon equation with properly defined asymptotic states. This framing reveals two distinct scenarios. In the first, time flows forward through the bounce: the universe contracts, reaches maximum density, and expands, with the internal time arrow pointing the same direction throughout. In the second, time reverses at the bounce: the contracting phase runs time one way, the expanding phase runs it the other.
The first scenario — time flowing forward — diverges at high energies. The Wheeler-DeWitt theory is valid only up to a threshold; beyond it, the equations produce infinities and the theory requires regularization it cannot provide. This is exactly where the bounce is supposed to work. The theory fails at the energy scale where the singularity lives.
The second scenario — time reversing — is well-posed at every energy scale, at least to first perturbative order. No divergences, no threshold. The ekpyrotic bounce with temporal reversal handles arbitrarily high energies without breaking.
The asymmetry is stark. Maintaining causality through the crisis requires physics that doesn't exist yet. Reversing causality through the crisis works with the physics we have. The universe's mathematically safest route through its most extreme moment is to flip its arrow of time. Running backwards is more robust than running forwards.
Whether this is physical or an artifact of the Wheeler-DeWitt framework is open. But the mathematical fact stands: in quantum cosmology, temporal reversal costs less than temporal continuity.