f(R, $G$, T) Gravity: Cosmological Implications and Dynamical System Analysis

We consider the cosmological implications of a four-dimensional extension of the Gauss-Bonnet $f(G)$ gravity, where $G$ is the Gauss-Bonnet topological invariant, in which the Einstein-Hilbert action is replaced by an arbitrary function $f(R,G,T)$ of G, of the Ricci scalar $R$, and of the trace $T$ of the matter energy-momentum tensor. By construction, the extended Gauss-Bonnet type action involves a non-minimal coupling between matter and geometry. The field equations of the model are obtained by varying the action with respect to the metric. The generalized Friedmann equations, describing the cosmological evolution in the flat Friedmann-Lemaitre-Robertson-Walker geometry, are also presented in their general form. We investigate the cosmological evolution of the Universe in the generalized Einstein-Gauss-Bonnet theiry for a specific choice of the Lagrangian density, as given by $f(R,G,T) = \alpha_1 G^{m} + \alpha_2 R^{\beta} - 2\alpha_3 \sqrt{-T},$ where $\alpha_i$ $i = 1, 2, 3$), $m$, and $\beta$ are model parameters. First, the theoretical predictions of the model are compared with a set of observational data (Cosmic Chronometers, Type IA Supernovae, Baryon Acoustic Oscillations) via an MCMC analysis, which allows us to obtain constraints on the model parameters. A comparison with the predictions of the $\Lambda$CDM system is also performed. Next, the generalized Friedmann equations are reformulated as a dynamical system, and the properties of its critical points are studied by using the Lyapunov linear stability analysis. This investigation allows for the reconstruction of the Universe's history in this model, from the early inflationary era to the late accelerating phase. The statefinder diagnostic parameters for the model are also considered from the dynamical system perspective.