Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutions

TL;DR

This paper demonstrates how choosing the correct gauge is essential for analyzing the stability of non-singular bouncing cosmological solutions in Horndeski theories, revealing stable solutions involving null-energy condition violation.

Contribution

It introduces a gauge choice that allows for stable, non-singular bounce solutions in Horndeski theories, bridging modified gravity and Einstein gravity regimes.

Findings

Stable bounce solutions with null-energy condition violation.

Proper gauge choice ensures classical stability of all modes.

Solutions connect modified gravity and Einstein gravity regimes.

Abstract

In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions with classically stable behavior for all modes with wavelengths above the Planck scale where: (a) the solution involves a stage of null-energy condition violation during which gravity is described by a modification of Einstein's general relativity; and (b) the solution reduces to Einstein gravity both before and after the null-energy condition violating stage. Similar considerations apply to galilean genesis scenarios.