Reconciling Fractional Power Potential and EGB Gravity in the light of ACT

Abstract: Recent results from the ACT collaboration indicate a higher value for the scalar spectral index, with $n_s = 0.9743 \pm 0.0034$, which sets tighter constraints on inflationary models, and these shifts are not in favor of many pre existing scenarios, including the widely studied and accepted standard Starobinsky model. In this paper, we examine the fractional power scalar potential within the framework of Einstein Gauss Bonnet (EGB) gravity, incorporating standard slow roll approximation. The EGB theory, motivated by higher dimensional models, introduces quadratic curvature corrections and a coupling between the scalar field and the Gauss Bonnet term, thereby modifying the cosmological dynamics. The results show good agreement with observational data, placing the predictions within the $1 \sigma$ region of the ACT $r-n_s$ constraint plot. Furthermore, incorporating the running of the scalar spectral index reinforces the models consistency with observational bounds. We also explore the parameter space of the EGB couplings and identify the range of free parameters for which the results of $n_s$ and $r$ values remain within the $1 \sigma$ region of the ACT constraints. Finally, we also investigate the reheating phase, demonstrating that the model not only agrees with ACT data but also satisfies the lower bound on the reheating temperature, thereby ensuring a consistent and viable cosmological scenario.