Spacetimes with vector distortion: Inflation from generalised Weyl geometry

TL;DR

This paper introduces a new class of non-Riemannian geometries with vector distortion, leading to a novel inflationary model that extends Starobinsky inflation and includes ghost-free vector-tensor interactions.

Contribution

It develops a general framework for spacetimes with vector distortion, extending Weyl geometry, and derives a unique inflationary model with quadratic curvature corrections.

Findings

Results in a one-parameter extension of Starobinsky inflation.

Introduces ghost-free vector-tensor interactions in quadratic curvature actions.

Generalizes conformal Weyl geometry with new geometric structures.

Abstract

Spacetime with general linear vector distortion is introduced. Thus, the torsion and the nonmetricity of the affine connection are assumed to be proportional to a vector field (and not its derivatives). The resulting two-parameter family of non-Riemannian geometries generalises the conformal Weyl geometry and some other interesting special cases. Taking into account the leading order quadratic curvature correction to the Einstein-Hilbert action results uniquely in the one-parameter extension of the Starobinsky inflation known as the alpha-attractor. The most general quadratic curvature action introduces, in addition to the canonical vector kinetic term, novel ghost-free vector-tensor interactions.