Dynamical Systems Analysis of an Einstein–Cartan Ekpyrotic Nonsingular Bounce Cosmology

Submitted to General Relativity and Gravitation (2025) — Preprint available: arXiv:2512.11885

• In this work I build a concrete early-universe model in Einstein–Cartan gravity where the Big Bang singularity is replaced by a smooth bounce. The key ingredients are a steep ekpyrotic scalar field and a Weyssenhoff spin fluid whose spin–torsion coupling produces a repulsive effect at very high density. The goal is not just to write down a bouncing solution, but to ask whether such a bounce is dynamically stable once anisotropies and curvature are included.

• I extend the standard Copeland–Liddle–Wands dynamical system to a six-dimensional phase space that tracks the scalar field, anisotropic shear, spatial curvature, and spin–torsion density. From this system I derive the full 6×6 Jacobian and analyze the fixed points controlling contraction, bounce, and expansion. A central result is the identification of a “Basin of Viability” in parameter space where the ekpyrotic phase suppresses the usual BKL shear instability and the spin–torsion term drives a nonsingular bounce instead of chaotic Mixmaster behavior.

• To test the dynamical systems picture, I develop a Python pipeline using stiff implicit Radau IIA integrators to evolve the Friedmann–Cartan equations through the high-curvature regime and across H = 0. The numerical solutions agree with the phase-space analysis and exhibit a controlled transition from contraction to expansion at finite scale factor. The paper closes by outlining implications for the primordial tensor spectrum: the stiff ekpyrotic phase naturally produces a blue-tilted gravitational-wave background, which could in principle shift part of the signal into the frequency band of ground-based interferometers.