# A class of regular bouncing cosmologies

## TL;DR

This paper introduces a new class of regular bouncing cosmological models using four scalar fields in geometric sigma models, ensuring stability and negligible graviton mass, overcoming previous singularity issues.

## Contribution

The paper develops a novel class of singularity-free bouncing cosmologies with stable perturbations using four scalar fields, advancing beyond previous models with fewer fields.

## Key findings

- Models are free of singularities across all backgrounds.
- Perturbation dynamics include 2 tensor, 2 vector, and 2 scalar degrees of freedom.
- Graviton mass can be made arbitrarily small, well below experimental bounds.

## Abstract

In this paper, I construct a class of everywhere regular geometric sigma models that possess bouncing solutions. Precisely, I show that every bouncing metric can be made a solution of such a model. My previous attempt to do so by employing one scalar field has failed due to the appearance of harmful singularities near the bounce. In this work, I use four scalar fields to construct a class of geometric sigma models which are free of singularities. The models within the class are parametrized by their background geometries. I prove that, whatever background is chosen, the dynamics of its small perturbations is classically stable on the whole time axes. Contrary to what one expects from the structure of the initial Lagrangian, the physics of background fluctuations is found to carry 2 tensor, 2 vector and 2 scalar degrees of freedom. The graviton mass, that naturally appears in these models, is shown to be several orders of magnitude smaller than its experimental bound. I provide three simple examples to demonstrate how this is done in practice. In particular, I show that graviton mass can be made arbitrarily small.