Bouncing Theory in the Modified $f(R,G,T)$ Gravity

In this study, we explore the dynamics of the universe using a modified gravity model represented by $f(R, G, T)$, where $R$ is the Ricci scalar, $G$ is the Gauss-Bonnet invariant, and $T$ is the trace of the stress-energy tensor. The model incorporates two scalar fields and is analyzed within a flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe. We derive the equations of motion, energy-momentum tensor components, energy density, and pressure while establishing conservation laws. Using the Einstein field equations, we obtain modified Friedmann equations and simplify their solutions. We emphasize crossing the phantom divide line (PDL) of the equation of state (EoS) parameter and reversing the scale factor and Hubble parameter at $t = 0$ to resolve the singularity problem by proposing a bouncing cosmology, thereby exploring early universe dynamics without an initial singularity. By analyzing five samples $f(R, G, T)$ models, we reconstruct their effective energy density and pressure, demonstrating the significance of crossing the PDL. Our framework generalizes other theories, including conformally modified Weyl gravity, and is validated through numerical calculations and graphical results.