Stability Analysis of Four $f(Q)$ Gravity Models : A Cosmological Review in the Background of Bianchi-I Anisotropy

Abstract

With the non-metricity scalar $Q$ as the functional argument, several $f(Q)$ gravity models are found to be proposed which are perfectly able to mimic the late-time accelerated expansion as pointed out by the type Ia supernovae observations. Temperature fluctuation differences for two celestial hemispheres, Hubble tension, voids, dipole modulation, anisotropic inflation, etc. motivates us to think beyond the $\Lambda$CDM model and the cosmological principle. Bianchi-I model portrays an anisotropic universe imposing shear. $f(Q)$ model also enables us to produce early inflation to late de Sitter universe without the requirement of $\Lambda$CDM. Ambiguities regarding fine-tuning or coincidences can be avoided alongwith. So, this article finds different stationary points of cosmic evolution with $f(Q)$ models habilitating in Bianchi-I anisotropic universe. Depending on models' nature, fixed points with different categories are found. Perturbations are followed wherever are applicable. While pursuing cosmological implications towards these fixed points, some are found to be formed only for the consideration of $f(Q)$ gravity and Bianchi-I both. Besides different prediction towards early inflation to late-time expansion which are available in existing literature of dynamical system studies, occurances of ultra slow roll inflation is predicted. For particular $f(Q)$ model, shear is predicted to decay leaving behind a constant valued residue. This models a universe that gradually turns more homogeneous. In some other models, depending on initial conditions, a final isotropic leftover is marked as the future fate of anisotropic world. More than one stable points are marked for special cases and are cosmologically interpreted.