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

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

2001-04-12

arxiv.org/abs/gr-qc/0104033v3

Phys.Rev.D65:024014,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12pages, 1 figure, typos corrected, a couple of paragraphs modified but no major change in the text, final version to be publi

Scientific paper

10.1103/PhysRevD.65.024014

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.

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