This work explores the stability of the Einstein Universe in the framework of Formula: see text gravity, where matter and geometry are directly coupled. Using the closed Bianchi IX geometry, we derive and linearize the field equations under minimally coupled model, i.e., Formula: see text. This leads to coupled fourth-order differential equations that describe the behavior of small anisotropic perturbations. To capture different coupling effects, we examine four models, a linear model Formula: see text, representing the simplest extension of GR, a quadratic model Formula: see text, which incorporates higher-order matter contributions, an inverse trace model Formula: see text, with the inverse depending on the trace Formula: see text and a logarithmic model Formula: see text, with an interplay between curvature and matter. Both conserved and non-conserved forms of the energy momentum tensor are analyzed. The results, illustrated through graphs, show that stability depends on the matter-geometry coupling, the equation of state, and the chosen model. Conserved cases are more restrictive, while non-conserved cases allow broader regions of stability. Overall, the study indicates that matter geometry interaction can act as a stabilizing mechanism beyond GR and supports Formula: see text gravity as a meaningful alternative to dark energy in explaining cosmic acceleration.
Alshammari et al. (Thu,) studied this question.
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