Bouncing Cosmology in 1+1 Dimensions

TL;DR

This paper constructs a non-singular bouncing cosmology in 1+1 dimensions by analyzing the backreaction of winding condensates, ensuring geodesic completeness and avoiding singularities through analytic continuation and smooth coordinate transformations.

Contribution

It introduces a novel 1+1 dimensional bouncing cosmological model derived from Euclidean black hole backreaction, ensuring non-singularity and weak coupling conditions.

Findings

Obtained non-singular solutions at near-Hagedorn temperatures.

Connected solutions via smooth coordinate transformation to maintain weak coupling.

Model is geodesically complete and free of singularities.

Abstract

In this paper, I construct a bouncing cosmology by considering the backreaction of the winding condensate on a 1+1 dimensional cosmological model with a periodic spatial coordinate. I based my work on previous results that considered the backreaction of the winding condensate on a 1+1 dimensional Euclidean black hole. This cosmological model is obtained as an analytic continuation of a Euclidean black hole. I solved the equations and obtained non-singular solutions at near-Hagedorn temperatures, both numerically and analytically. To remain within the weak coupling regime, it is necessary to connect two solutions; otherwise, the dilaton, which determines the string coupling, would grow quadratically. This connection is achieved through a smooth coordinate transformation, ensuring the model's validity. As a result, the model becomes geodesically complete and non-singular. The connection is made at a time in which the curvature is small, thereby avoiding higher-order $\alpha'$ corrections.