Reheating constraints for an induced gravity model with a holographic description

In this paper, we investigate an induced gravity model embedded in a holographic framework with a focus on a quadratic potential during the reheating phase. Although the reheating phase cannot be directly probed through cosmological observations, it can be indirectly constrained by studying the evolution of CMB modes from their horizon exit during inflation to the present time. In this setting, the reheating epoch is characterized by three essential parameters: the reheating temperature $T_{\text{re}}$, the number of e-folds during reheating, $N_{\text{re}}$, and the effective equation of state parameter, ${\omega }_{\text{re}}$. These parameters provide a crucial link between the inflationary dynamics and the onset of the standard hot big bang phase. We derive meaningful constraints on the braneworld inflationary model by comparing how well our results align with the recent cosmological constraints from the combined dataset, incorporating Atacama Cosmology Telescope (ACT) DR6, Planck 2018, BICEP/Keck 2018 and DESI data (P-ACT-LB-BK18). To further examine the role of holographic cosmology in the reheating era, particularly after including induced gravity corrections on the brane, we analyze the reheating constraints for selected values of the holographic and induced gravity parameters, assuming fixed values of ${\omega }_{re}$ within the range $-1/3\le {\omega }_{re}<1/3$. Under these conditions, and for the specific parameter choices $c\le 4\times 10^7$ and $0.2<\gamma \le 0.6$, our model produces results consistent with the latest observations. The reheating duration corresponds to the central value of the spectral index and satisfies the lower bound on the reheating temperature, thereby ensuring a consistent and physically viable cosmological scenario.