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

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 m² = V″(φ). We decompose the bulk scalar field into the infinite mass spectrum of four-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 ²lm² ≪ 1, where l̄ is the curvature radius of the effectively anti-de Sitter bulk, but it is violated if |l̄m ²lm², though the violation is very small. Then we evaluate the vacuum expectation value 〈δφ²〉 on the brane. We find the zero-mode contribution completely dominates if |m ²l̄² ≪ 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 |m²|l̄² is large.