Enhancing inflationary model predictions via refined slow-roll dynamics

Abstract: The inflationary paradigm not only addresses early Universe puzzles but also aligns well with the observational constraints, with slow-roll inflationary models fitting best. Evaluating these model predictions requires considering both slow-roll inflationary dynamics and the subsequent reheating epoch. This involves the quantitative analysis that takes into account the effective equation of state (EoS) and duration of reheating, connecting these with the perturbations generated deep during the inflationary era. Given the complexities involved, many approximations are often used for simplification. However, as future observations are expected to improve the accuracy of these observables significantly, this work takes a different approach. Instead of relying on approximations, we consider the near-accurate solutions of inflationary models and compare our results with the pre-existing ones. It mainly incorporates two improvements: the first is the accurate dynamics of the slow-roll evolution, and, thus, the end of inflation; and the second is the higher-order slow-roll corrections to the perturbed observables. Our findings indicate that, by implementing these corrections, the theoretical predictions improve significantly. It also indicates that seemingly minor corrections can have significant effects on the perturbed observables, and these refined predictions can be compared with future observations to potentially rule out models and help resolve the degeneracy problem of the inflationary paradigm.