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 ${\mathcal{D}}_{ab}$ 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.

39 pages, 9 figures, added background material on coadjoint orbits of Virasoro algebra that demonstrates the string-inspired nature of the model, made various minor edits and corrections

References in corpus (6)

• The Standard Model Higgs boson as the inflaton
• Conformal Transformations with Multiple Scalar Fields
• Inflation by non-minimal coupling
• Reheating of the universe after inflation with f(phi)R gravity
• Relaxing inflation models with non-minimal coupling: A general study
• General structure of Thomas$-$Whitehead gravity

Cited by in corpus (2)

• Covariant and Manifestly Projective Invariant Formulation of Thomas-Whitehead Gravity
• Constraint Analysis and Quantization of Anomalous 2-D Thomas-Whitehead Gravity