Cosmological singularities in conformal Weyl gravity

Yaghoub Heydarzade

doi:10.1140/epjc/s10052-019-7446-4

Abstract

In this work, we study the issue of the past and future cosmological singularities in the context of the fourth-order conformal Weyl gravity. In particular, we investigate the emergent universe scenario proposed by Ellis et al., and find the stability conditions of the corresponding Einstein static state using the fixed point approach. We show that depending on the values of the parameters of the conformal Weyl gravity theory, there are possibilities for having initially stable emergent states for an FRW universe with both the positive and negative spatial curvatures. This represents that the conformal Weyl gravity can be free of the initial singularity problem. Then, following Barrow et al., we address the possible types of the finite-time future cosmological singularities. We discuss how these singularities also can be avoided in the context of this theory.

Highlights

For the past singularity problem, we investigated the emergent universe scenario proposed by Ellis et al We obtained the stability conditions for the corresponding Einstein static universe (ESU) using the fixed point approach
We showed that depending on the values of the parameters of the conformal Weyl gravity theory, there are possibilities for having initially stable ESUs for an FRW universe with both the positive and negative spatial curvatures
It is found that there exists the possibility of having ESU for the ordinary matter fields possessing the equation of state ω ≥ 0, but the conformal Weyl theory is not capable to have a non-singular spatially flat ESU

Summary

Introduction

After the discovery of the accelerating expansion of the universe, deeper studies of the features of the cosmic fluid responsible for this accelerating expansion, the so called “dark energy”, showed the plethora of new types of singularities different than the initial big bang singularity. One may refer to the recent work of Maldacena [42] where it is shown that in the four dimension, the conformal gravity with a Neumann boundary condition is classically equivalent to the Einstein gravity with a cosmological constant It has been suggested by Kazanas and Mannheim that the conformal Weyl gravity can be considered an independent theory on its own right instead of looking for a low energy GR limit. In order to check the viability of the conformal Weyl gravity, the deflection of light and time delay in the exterior of a static spherically symmetric source were investigated in [52,53], and it was found that the parameters of the theory fit the experimental constraints It is shown in [54] that one can find a class of wormhole geometries satisfying the energy conditions in the neighborhood of the throat of wormhole.

Conformal Weyl gravity theory

The possible future singularities

Conclusion