Asymmetric cyclic evolution in polymerised cosmology

TL;DR

This paper uses dynamical systems methods to analyze polymerised scalar field cosmologies with a cosmological constant, revealing generic cyclic solutions and deriving exact solutions, with behavior depending on the sign and value of the cosmological constant.

Contribution

It provides a comprehensive dynamical analysis of polymerised cosmologies, identifying conditions for cyclic behavior and deriving exact solutions, which advances understanding of quantum gravity effects in cosmology.

Findings

Cyclic solutions are shown to be generic in polymerised cosmology.

The sign of the cosmological constant determines cyclic or non-cyclic behavior.

An upper bound on the cosmological constant is derived from the dynamical analysis.

Abstract

The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase space. We have shown that the cyclic solutions are generic. The exact solution for polymerised cosmology is also obtained. Two basic cases are investigated, the polymerised scalar field and the polymerised gravitational and scalar field part. In the former the division on the cyclic and non-cyclic behaviour is established following the sign of the cosmological constant. The value of the cosmological constant is upper bounded purely from the dynamical setting.