Timelike Vector Field Dynamics in the Early Universe

TL;DR

This paper explores the behavior of a timelike vector field during the early universe's inflationary phase, analyzing its dynamics and perturbation spectra, especially under different coupling conditions, to understand its role in cosmology.

Contribution

It investigates the evolution of a timelike vector field in inflationary models and calculates its power spectrum without metric perturbations, highlighting conditions for scale invariance.

Findings

Time component perturbations are scale invariant at ξ=0.

Longitudinal and transverse perturbations are scale invariant at ξ=1/6.

Timelike vector fields are challenging to realize during inflation.

Abstract

We study the dynamics of a timelike vector field which violates Lorentz invariance when the background spacetime is in an accelerating phase in the early universe. It is shown that a timelike vector field is difficult to realize an inflationary phase, so we investigate the evolution of a vector field within a scalar field driven inflation model. And we calculate the power spectrum of the vector field without considering the metric perturbations. While the time component of the vector field perturbations provides a scale invariant spectrum when $\xi = 0$, where $\xi$ is a nonminimal coupling parameter, both the longitudinal and transverse perturbations give a scale invariant spectrum when $\xi = 1/6$.