Dynamical systems approach and cosmological attractors in newer general relativity

TL;DR

This paper analyzes the cosmological dynamics of newer general relativity theories using dynamical systems, identifying various attractors and behaviors such as big rip, turnaround, and eternal expansion, influenced by effective dark energy properties.

Contribution

It provides a comprehensive dynamical systems analysis of newer general relativity theories, revealing their fixed points, asymptotic behaviors, and cosmological attractors in vacuum flat FLRW models.

Findings

Different theories exhibit scenarios like big rip, turnaround, and eternal expansion.

The effective dark energy barotropic index determines the universe's fate, showing phantom or non-phantom behavior.

The analysis includes complete solution spaces and phase diagrams for specific subclasses.

Abstract

We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as ``newer general relativity'' using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat Friedmann-Lema\^itre-Robertson-Walker metric. For the most general class of theories, we study generic properties of the solutions, in particular their fixed points, asymptotic behavior and effective dark energy. We then apply this approach to two phenomenologically motivated subclasses of theories, which we study in full detail. For these theories, we derive the complete space of solutions and cosmological attractors, which we display in a number of phase diagram. Depending on the particular theory at hand, we find different possible scenarios, including a turnaround followed by a big crunch, a big rip and an eternally expanding universe whose Hubble parameter asymptotically approaches zero. It turns that this different behavior can be explained by the effective dark energy barotropic index, which shows either phantom or non-phantom behavior, depending on the theory, but does not change dynamically between these two possibilities.