Inflation from dynamical projective connections

Abstract

We show how the recently developed string-inspired, projectively invariant gravitational model Thomas-Whitehead gravity (TW gravity) naturally gives rise to a field acting as the inflaton. In the formulation of TW gravity, a field Dab is introduced into the projective connection components and is related to a rank-two tensor field Pab. Through the dynamical action of TW gravity, in terms of projective curvature, the tensor field Pab acquires dynamics. By decomposing Pab into its trace and traceless degrees of freedom, and choosing the connection to be Levi-Civita, we demonstrate that TW gravity contains a nonminimally coupled scalar field with a specific potential. Considering only the trace degrees of freedom, we demonstrate that the scalar field acts as an inflaton in the slow-roll approximation. We find a range of values for the parameters introduced by TW gravity that fit the experimental constraints of the most recent cosmological data.