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

Norichika Sago·Yoshiaki Himemoto·Misao Sasaki
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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 $ϕ$ with $m^2=V''(ϕ)$. 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 $<δϕ^2>$ 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.

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Norichika Sago, Yoshiaki Himemoto, Misao Sasaki. 2001-11-09. Quantum fluctuations in brane-world inflation without inflaton on the brane. https://doi.org/10.1103/physrevd.65.024014

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