Dynamical analysis of the covariant $f(Q)$ gravity models

TL;DR

This paper investigates covariant $f(Q)$ gravity models with dynamic coupling functions, analyzing their ability to reproduce the Universe's evolution through critical points and phase space analysis.

Contribution

It introduces specific power-law and logarithmic $f(Q)$ models, analyzes their stability, and demonstrates their consistency with cosmic evolution including late-time acceleration.

Findings

Both models reproduce radiation, matter, and dark energy eras.

Stability of critical points is established via dynamical systems analysis.

Phase space trajectories support the models' viability for cosmic evolution.

Abstract

In this study, we explore the cosmological evolution of the Universe in the framework of covariant $f(Q)$ gravity, with a coupling function that evolves dynamically in proportion to the Hubble parameter. Two specific forms of the function are examined: a power-law model and a logarithmic model. By rewriting the cosmological field equations as an autonomous dynamical system, we determine and classify the corresponding critical points and analyze their stability. Our results show that both models are able to reproduce the sequence of cosmic evolution, including radiation, matter, and dark energy-dominated eras, along with the transitions between them. The physical properties at each critical point are described using key cosmological quantities such as the total EoS parameter, density parameters, and the deceleration parameter. The stability of the non-hyperbolic critical point is analyzed through center manifold theory. In addition, we present phase space trajectories along with the stability behavior of each critical point. The evolution plots for the density parameters of radiation, matter, and dark energy, along with the EoS parameter for the total, are illustrated for further analysis. Overall, the analysis suggests that the $f(Q)$ models considered here, within the context of covariant formulation, provide a consistent description of cosmic evolution and offer a promising approach to explaining the late-time acceleration of the Universe.