The Inflationary Quartic Hilltop Model in a Modified Gravity and Its Comparison with the Observations

Abstract

We investigate the inflation for the quartic hilltop model via a certain type of modified gravity. Precisely, we analyze the $F(\ddot{I}•)T$ term in the Einstein's gravity to examine the quartic hilltop inflation model. $T$ is the trace of the energy-momentum tensor, and $\ddot{I}•$ is the inflaton field. Next, we calculate the inflation dynamics for the foregoing model and obtain the slow-roll parameters, i.e., the scalar spectral index ``$n_s$'' and the tensor-to-scale ratio ``$r$'', which these parameters exhibit high sensitivity to the $F(\ddot{I}•)T$ term. This modified form of the gravity is not only in accordance with the predictions of the original model but also allows for better prediction of the Planck/BICEP/Keck data.

21 pages, LaTex2e, 4 figures