Initial Kaluza-Klein fluctuations and inflationary gravitational waves in braneworld cosmology

TL;DR

This paper investigates how initial Kaluza-Klein quantum fluctuations influence the spectrum of inflationary gravitational waves in braneworld cosmology, finding they have negligible impact on late-time observations regardless of inflationary energy scales.

Contribution

It demonstrates through numerical analysis that initial Kaluza-Klein fluctuations do not significantly affect the gravitational wave spectrum in Randall-Sundrum braneworld models.

Findings

Kaluza-Klein fluctuations have minimal impact on late-time gravitational wave spectrum.

The result holds across various inflationary energy scales.

Numerical methods confirm the negligible effect of initial KK modes.

Abstract

We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wronskian formulation.