Gravity waves from inflating brane or Mirrors moving in adS$_5$

TL;DR

This paper investigates tensor perturbations and graviton creation during inflation in a brane-world model with an anti-de Sitter bulk, finding that the graviton spectrum largely resembles four-dimensional predictions with minor Kaluza-Klein contributions.

Contribution

The study demonstrates that the vacuum state for gravitons is consistent across different frames and analyzes graviton production, showing the spectrum aligns with four-dimensional results with small extra-dimensional effects.

Findings

Vacuum states are equivalent in static adS$_5$ and dS$_4$ frames.

Graviton production during brane inflation matches four-dimensional theory.

Kaluza-Klein graviton production is subdominant.

Abstract

We study tensor perturbations in a model with inflating Randall--Sundrum-type brane embedded in five-dimensional anti-de Sitter (adS$_5$) bulk. In this model, a natural {\it in}-vacuum of gravitons is the vacuum defined in static adS$_5$ frame. We show that this vacuum is, in fact, the same as the {\it in}-vacuum defined in the frame with de Sitter (dS$_4$) slicing, in which the brane is at rest. Thus, during inflation, gravitons on and off the brane remain in their vacuum state. We then study graviton creation by the brane on which inflation terminates at some moment of time. We mostly consider gravitons whose wavelengths at the end of inflation exceed both the horizon size and the adS$_5$ radius. Creation of these gravitons is dominated by (zero mode)--(zero mode) Bogoliubov coefficients and, apart from an overall factor, the spectrum of produced gravitons is the same as in four-dimensional theory. ``Kaluza--Klein'' gravitons are also produced, but this effect is subdominant. Graviton spectra at somewhat higher momenta are also presented for completeness.