Cosmological Perturbations in Inflationary Models with Anisotropic Space-Time Scaling in Lifshitz Background

TL;DR

This paper develops a cosmological perturbation theory for inflationary models with anisotropic Lifshitz backgrounds, revealing unique gravitational wave behaviors and potential observational signatures in lensing and CMB.

Contribution

It introduces a consistent perturbation framework for anisotropic Lifshitz inflationary models with broken four-dimensional covariance, highlighting novel gravitational wave and potential observational effects.

Findings

Gravitational waves propagate with variable speeds, including superluminal cases.

Bardeen and Newtonian potentials differ, affecting lensing and CMB.

Inflaton excitations vanish at linear order.

Abstract

Models of inflation in a gravitational background with an anisotropic space-time scaling are studied. The background is a higher-dimensional Lifshitz throat with the anisotropy scaling $z\neq 1$. After the dimensional reduction, the four-dimensional general covariance is explicitly broken to a three-dimensional spatial diffeomorphism. As a result the cosmological perturbation theory in this set up with less symmetries have to be formulated. We present the consistent cosmological perturbation theory for this set up. We find that the effective four-dimensional gravitational wave perturbations propagate with a different speed than the higher dimensional gravitational excitations. Depending on the model parameters, for an observer inside the throat, the four-dimensional gravitational wave propagation can be superluminal. We also find that the Bardeen potential and the Newtonian potential are different. This can have interesting observational consequences for lensing and CMB fluctuations. Furthermore, we show that at the linearized level the inflaton field excitations vanish.