Dynamical Systems Analysis of f(R,G) Cosmological Model with Dark Sector Coupling

In this article, we examine the dynamical system of the $f(R,\mathcal{G})$ gravity model. This $f(R,G)$ model framework is composed of interactions between dark matter and scalar field through the linear coupling term. The key objective of the present study is to describe the cosmological viability of the modified gravity theory formulated with the gravity $f(R,\mathcal{G})$. We transform the cosmological equations into an autonomous system of ordinary differential equations by suitable transformation of variables. The $f(R,\mathcal{G})$ model governed by $f(R,\mathcal{G})=\alpha R^m+\beta {\mathcal{G}}^n$ has been investigated in detail to characterize the stability properties of the critical points of the autonomous system. The model may explain the late-time accelerating universe expansion corresponding to the attractor in model. Depending on the effective equation of state parameter values corresponding to the critical points, we study the observational viability of the model using low-redshift observational data such as the observational Hubble data. Furthermore, we investigate the effects of parameters by using the effective equation of state parameter and statefinder diagnostics.