Geodesically Complete Curvature-Bounce Inflation

TL;DR

This paper constructs a geodesically complete closed universe model with a bounce and inflation driven by a canonical scalar field, consistent with current observational constraints and without exotic matter.

Contribution

It presents the first explicit model of a complete, geodesically complete closed universe with a bounce and inflation driven solely by ordinary matter satisfying the NEC.

Findings

Supports a nonsingular bounce with positive spatial curvature.

Predicts inflationary observables consistent with current data.

Shows regular propagation of perturbations through the bounce.

Abstract

The early universe need not be described by an incomplete inflationary phase connected to a separate, more exotic prehistory. Recent results show that, within non-static FRW cosmology, only positive spatial curvature permits a nonsingular, geodesically complete universe with ANEC-respecting matter. We construct a geodesically complete closed $k=+1$ bounce-plus-inflation cosmology in ordinary general relativity, sourced by a single canonical scalar field with a positive vacuum offset. The bounce is supported by curvature rather than exotic stress energy: the matter content satisfies the NEC throughout and violates only the strong energy condition, as in any accelerated expansion. The solved branch remains sub-Planckian and evolves onto a curvature-diluted slow-roll phase with inflationary observables consistent with current constraints. The pivot-scale predictions are $n_s=0.9617$, $r=0.0045$ at $N_*=55$ and $n_s=0.9650$, $r=0.0037$ at $N_*=60$. Direct evolution of closed-universe infrared perturbations shows regular tensor and scalar propagation through the bounce and inflationary era, with the physical curvature perturbation freezing in the standard way. This gives a minimal explicit realization of a complete early-universe cosmology in the closed FRW branch selected by completeness and ANEC compatibility.