A classical, non-singular, bouncing universe

TL;DR

This paper introduces a classical, non-singular bouncing universe model within General Relativity that avoids NEC violation, using a scalar field coupled to curvature, resulting in a geodesically complete, stable cosmology.

Contribution

The paper presents a novel bouncing cosmology model with positive spatial curvature and scalar-curvature coupling, avoiding NEC violation and singularities, while remaining within effective field theory limits.

Findings

The universe bounces without NEC violation.

The model is free of ghost and tachyonic instabilities.

It solves the horizon problem and is geodesically complete.

Abstract

We present a model for a classical, non-singular bouncing cosmology without violation of the null energy condition (NEC). The field content is General Relativity plus a real scalar field with a canonical kinetic term and only renormalizable, polynomial type self-interaction for the scalar field in the Jordan frame. The universe begins vacuum-energy dominated and is contracting at $t=-\infty$. We consider a closed universe with a positive spatial curvature, which is responsible for the universe bouncing without any NEC violation. An $R\phi^2$ coupling between the Ricci scalar and the scalar field drives the scalar from the initial false vacuum to the true vacuum during the bounce. The model is sub-Planckian throughout its evolution and every dimensionful parameter is below the effective field theory scale $M_P$, so we expect no ghost-type or tachyonic instabilities. This model solves the horizon problem and extends co-moving particle geodesics to past infinity, resulting in a geodesically complete universe without singularities. We solve the Friedman equations and the scalar field equation of motion numerically, and analytically under certain approximations.