Inflation from Dynamical Projective Connections

TL;DR

This paper shows that a string-inspired, projectively-invariant gravitational model naturally produces an inflaton field capable of driving cosmic inflation, fitting recent cosmological data through specific parameter choices.

Contribution

It introduces a novel connection between TW gravity and inflation, demonstrating how the model's scalar field acts as an inflaton consistent with observational constraints.

Findings

The scalar field in TW gravity can serve as an inflaton.

The model's parameters can be tuned to match cosmological data.

TW gravity provides a new geometric framework for inflation.

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 $\mathcal{D}_{ab}$ is introduced into the projective connection components and is related to a rank-two tensor field $\mathcal{P}_{ab}$. Through the dynamical action of TW gravity, in terms of projective curvature, the tensor field $\mathcal{P}_{ab}$ acquires dynamics. By decomposing $\mathcal{P}_{ab}$ into its trace and traceless degrees of freedom, and choosing the connection to be Levi-Civita, we demonstrate that TW gravity contains a non-minimally 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.