Phase Space Analysis in f (Q) Gravity with Bulk Viscous Fluid

Abstract

The standard formulation of general relativity needs to be revised in explaining several re- cent phenomena observed in the universe. It motivates us to go beyond the standard idea of gravity. The f (Q) gravity theory is a fascinating modified theory of gravity in which the non-metricity Q determines the gravitational interaction. The vanishing affine connections have been utilized only in the application of the modified f (Q) gravity theory to cosmol- ogy. As a result, researchers were unable to compete with the current understanding of f (τ) theory earlier. In this work, we investigate a newly suggested approach to deal with this issue by studying the proposed construction of f (Q) theory utilizing a non-vanishing affine connection in the spatially flat FLRW space-time. We use a few variables and di- mensionless parameters to formulate the appropriate equations for the dynamical system approach. The conservation of the energy-momentum tensor leads to a constraint equation that establishes a relationship between the dynamical variables. The objective of this study is to investigate the cosmological models that include the effect of bulk viscosity in the cosmic fluid using the framework of f (Q) gravity. We used three models of f (Q) under bulk viscous fluids, revealing the existence of both unstable and stable de-sitter solutions for rapid expansions at early and late-times. Furthermore, it determines the existence of unstable points for matter eras in the context of every f (Q) function, so illustrating that the presence of non-zero affine connections might be responsible for a true sequence of cosmic eras.