Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity

TL;DR

This paper explores non-local higher-derivative gravity theories that can resolve the Big Bang singularity, revealing stable inflationary and cyclic solutions with perturbative stability.

Contribution

It provides a detailed analysis of the dynamical properties of non-local gravity models, demonstrating their ability to produce non-singular, geodesically complete cosmological solutions.

Findings

Stable inflationary attractors with positive cosmological constant

Cyclic universe solutions with negative cosmological constant

Bounce solutions are free from perturbative instabilities

Abstract

One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular bouncing solutions. In this paper we study in more details the dynamical properties of the equations of motion for these theories of gravity in presence of positive and negative cosmological constants and radiation. We find stable inflationary attractor solutions in the presence of a positive cosmological constant which renders inflation {\it geodesically complete}, while in the presence of a negative cosmological constant a cyclic universe emerges. We also provide an algorithm for tracking the super-Hubble perturbations during the bounce and show that the bouncing solutions are free from any perturbative instability.