ACT-ing on inflation: Implications of non Bunch-Davies initial condition and reheating on single-field slow roll models

Abstract: We investigate a class of slow roll inflationary models in the light of the recent Cosmic Microwave Background constraints from Planck 2018, ACT DR6, DESI DR1, and BICEP/\textit{Keck} 2018. The combined dataset favors a higher value of the scalar spectral index $n_{\mathrm{S}}=0.9743 \pm 0.0034$, which places increased pressure on several conventional inflationary scenarios. In this study, we analyze the observational viability of various well-motivated models, including the $\alpha$-attractor E- and T-models, chaotic inflation, hilltop inflation, and natural inflation. We incorporate the effects of a post-inflationary phase of reheating and examine how the dynamics of reheating influence the predictions in the $n{\mathrm{S}}-r$ plane. We also impose a lower bound on the reheating temperature based on the constraint from the effective number of relativistic species ($\Delta{N}{\mathrm{eff}}$) arising from primordial gravitational waves. While reheating improves agreement with observations for some models, significant regions of parameter space remain disfavored. Finally, we explore the impact of a non Bunch-Davies initial state and demonstrate that it can substantially improve the fit to the $n_{_\mathrm{S}}-r$ data across a broader class of inflationary models, thereby offering a potentially viable mechanism for reconciling theory with the latest observations.