Cosmology with Distinct Functions $f$ of the Non-metricity Scalar $Q$ : A Dynamical System Approach

TL;DR

This paper analyzes various $f(Q)$ gravity models using a dynamical systems approach to identify stable and unstable cosmological solutions, providing insights into their potential evolution and observational consistency.

Contribution

It introduces a systematic dynamical systems analysis for different $f(Q)$ models in symmetric teleparallel gravity, highlighting stability properties and cosmological implications.

Findings

Existence of stable, unstable, and saddle fixed points in $f(Q)$ models.

Phase portraits illustrate possible cosmological evolutions.

Comparative analysis of different $f(Q)$ structures and their stability.

Abstract

Symmetric teleparallel gravity is one among the general relativistic trinity which deals with the non-metricity scalar $Q$. In the Einstein Hilbert action, a function of $Q$ is chosen to be the main contributory part of the Lagrangian and a modified theory of gravity is constructed. In literature, different structures of the function of $Q$ are found which sustain several astrophysical observations like Big Bang nucleosynthesis, late-time cosmic acceleration etc. Autonomous systems for each such models with different $f(Q)$ structures are constructed. Corresponding fixed points and their stability properties are studied. For every case, stable, unstable and saddle-type fixed points are found to exist. These points on the phase portraits are cosmologically analyzed. It is tried to justify which way the corresponding state may lead if the initial state is perturbed. A comparative study of different models is represented.