Quantum fluctuations in brane-world inflation without inflaton on the brane

TL;DR

This paper investigates quantum fluctuations of a bulk scalar field in a brane-world inflation model, analyzing the dominance of zero-mode versus Kaluza-Klein modes under different mass conditions.

Contribution

It provides a detailed analysis of quantum fluctuations in a brane-world inflation model driven by a bulk scalar field, highlighting the conditions for zero-mode dominance.

Findings

Zero-mode dominance holds if |m^2|*l^2 << 1.

Kaluza-Klein modes are small but non-negligible if |m^2|*l^2 is large.

Classical solutions are dominated by zero-mode under certain conditions.

Abstract

A Randall-Sundrum type brane-cosmological model in which slow-roll inflation on the brane is driven solely by a bulk scalar field was recently proposed by Himemoto and Sasaki. We analyze their model in detail and calculate the quantum fluctuations of the bulk scalar field $\phi$ with $m^2=V''(\phi)$. We decompose the bulk scalar field into the infinite mass spectrum of 4-dimensional fields; the field with the smallest mass-square, called the zero-mode, and the Kaluza-Klein modes above it with a mass gap. We find the zero-mode dominance of the classical solution holds if $|m^2|\bar\ell^2\ll1$, where $\bar{\ell}$ is the curvature radius of the effectively anti-de Sitter bulk, but it is violated if $|m^2|\bar\ell^2\gg1$, though the violation is very small. Then we evaluate the vacuum expectation value $<\delta\phi^2>$ on the brane. We find the zero-mode contribution completely dominates if $|m^2|\bar{\ell}^2\ll 1$ similar to the case of classical background. In contrast, we find the Kaluza-Klein contribution is small but non-negligible if the value of $|m^2|\bar{\ell}^2$ is large.