Cosmology for quadratic gravity in generalized Weyl geometry

TL;DR

This paper explores quadratic gravity in generalized Weyl geometry, analyzing cosmological solutions with vector fields, identifying de Sitter attractors, and examining stability and perturbations to constrain viable models.

Contribution

It introduces a new class of vector-tensor theories in generalized Weyl geometry, analyzing their cosmological implications and stability, with specific exact solutions and constraints.

Findings

De Sitter attractors identified in the models

Various exact solutions including dark energy and bounce scenarios

Constraints imposed by stability analysis exclude some solutions

Abstract

A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.