Modified gravity models for inflation: In conformity with observations

Abstract

We consider a modified gravity framework for inflation by adding to the Einstein-Hilbert action a direct $f(\ddot{I}•)T$ term, where $\ddot{I}•$ is identified as the inflaton and $T$ is the trace of the energy-momentum tensor. The framework goes to Einstein gravity naturally when the inflaton decays out. We investigate inflation dynamics in this $f(\ddot{I}•)T$ gravity (not to be confused with torsion-scalar coupled theories) on a general basis and then apply it to three well-motivated inflationary models. We find that the predictions for the spectral tilt and the tensor-to-scalar ratio are sensitive to this new $f(\ddot{I}•)T$ term. This $f(\ddot{I}•)T$ gravity brings chaotic and natural inflation into better agreement with data and allows a larger tensor-to-scalar ratio in the Starobinsky model.

16 pages, 3 figures. Match the version accepted for publication in PRD