Late-Time Cosmic Acceleration in Ricci-Gauss-Bonnet Gravity via Gradient Descent Optimization

Abstract

We study the late-time evolution of the Universe within the f(R,G) gravity framework, where R is the Ricci scalar and G is the Gauss-Bonnet term. To make the model tractable, we propose a parametrization scheme and determine its parameters using Gradient Descent, with constraints coming from the latest Cosmic Chronometer (CC) and Pantheon+ supernova data. Key cosmological indicators, namely the deceleration parameter q and the equation-of-state parameter w, show a clear transition from past deceleration to the present accelerated expansion. Interestingly, the equation-of-state parameter w remains above the phantom divide, indicating quintessence-like behavior consistent with current observations. Energy-condition analysis further supports this framework: the strong energy condition is violated, consistent with models allowing cosmic acceleration, whereas both the weak and null energy conditions remain satisfied. To test consistency, we also apply the Om(z) diagnostic, which distinguishes this model from the standard cosmological constant scenario and indicates a quintessence-dominated future evolution. Using the best-fit values, we estimate the age of the Universe, obtaining good agreement with independent astrophysical measurements. Overall, the results suggest that f(R,G) gravity provides a viable and self-consistent explanation for late-time cosmic acceleration when constrained using the combined CC and Pantheon+ datasets.