DOI: 10.11648/j.ijass.20261403.12 ISSN: 2376-7022

Cosmological Dynamics in Quadratic f(R,G) Gravity with a Periodically Evolving Deceleration Parameter

Dhajendra Rabha, Rajshekhar Baruah
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The late-time accelerated expansion of the Universe remains one of the major challenges in modern cosmology, motivating the exploration of modified theories of gravity as alternatives to the standard ΛCDM framework. In this work, we investigate the cosmological evolution of a spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) universe within the framework of f(R,G) gravity, where both the Ricci scalar R and the Gauss–Bonnet invariant G contribute to the gravitational dynamics. We consider quadratic corrections to the Ricci scalar and Gauss-Bonnet invariant, with (ξ) and (λ) denoting the corresponding coupling parameters. To obtain the cosmological solutions, the modified field equations are analyzed by adopting a periodically varying deceleration parameter through a suitable parametrization of the scale factor. The resulting cosmological model is examined in detail in terms of its expansion history, dynamical evolution, scalar field correspondence, and energy conditions. The model describes an initially singular Universe characterized by vanishing volume and divergent energy density, followed by a transition to an accelerated expansion phase. The evolution of the effective equation-of-state parameter indicates a quintessence-like behavior of the dark-energy sector during the relevant stages of cosmic evolution. Furthermore, the model gradually approaches the behavior of the standard ΛCDM cosmology at late times. The analysis of the energy conditions and cosmological parameters demonstrates that the proposed quadratic f(R,G) model provides a physically viable description of the observed late-time cosmic acceleration. These results indicate that the combined quadratic Ricci and Gauss–Bonnet corrections can provide an effective geometric mechanism for describing the accelerated expansion of the Universe without requiring a separate dark-energy component.

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