A TWO-SIDED ENTROPIC RICCI FLOW AND A SMOOTH CPT-SYMMETRIC BOUNCE IN FRW COSMOLOGY

We present a novel cosmological construction based on a two-sided Ricci flow extended by the Kuznetsov tensor, which rigorously admits a smooth bounce in a Friedmann–Robertson–Walker (FRW) spacetime. We prove the existence and uniqueness of local solutions for a flow with an entropic functional that is monotonic in both directions of the time parameter, providing a mathematically consistent framework for a CPT-symmetric cosmological bounce. The solution exhibits a mirror symmetry in time, yielding two opposite arrows of time that emerge naturally from the entropic structure. Near the bounce, the scale factor remains strictly positive, eliminating the classical singularity while preserving smoothness of curvature invariants. The effective energy density associated with the Kuznetsov tensor, ρK∼λ(t), changes sign across the bounce, producing a geometrical analogue of a dynamical dark energy component. While the primary results are purely geometric and mathematically rigorous, we outline potential physical interpretations: the model may serve as a framework for exploring the CPT-symmetric evolution of cosmological perturbations, with implications for the initial conditions of the universe and for information transfer across horizons. Observationally, the model reduces to a standard ΛCDM-like behavior in the current epoch if the characteristic timescale of λ(t) evolution is sufficiently large, consistent with existing CMB constraints. This work provides the first mathematically exact realization of a two-sided entropic bounce in FRW cosmology, establishing a foundation for further exploration of CPT-symmetric dynamics and the role of entropic functionals in gravitational systems.