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Abstract

In this article, we present a generic dynamical system formulation for Bianchi-I cosmology in the presence of an isotropic fluid within the coincident gauge connection branch and one of the non-coincident gauge connection branches of $f(Q)$ gravity theory. For both the connection branches under consideration, we start from the generic Bianchi-I cosmological field equations in $f(Q)$ and present a prescription of how one can construct an autonomous dynamical system in terms of the standard Hubble-normalized dimensionless dynamical variables once an $f(Q)$ theory is provided. Particular care has been taken to single out the physically viable regions in the phase space for each of the models under consideration. This results in the finding that, for both of the connection branches under consideration, the Kasner solution marginally violates the key physical viability condition of positive effective gravitational coupling ($f_Q>0$) for all the models considered, whereas a physically viable de-Sitter future attractor appears in all the models, except for the very special case of the monomial model within the coincident gauge connection. In the context of the early universe cosmology, we find that isotropization of a homogeneously perturbed inflating FLRW universe is a generic model-independent feature in the coincident gauge, whereas the isotropization of a homogeneously perturbed pre-bounce ekpyrotically contracting FLRW universe is, although not completely generic, but a likely scenario.