Bulk scalar field in the braneworld can mimic the 4D inflaton dynamics

TL;DR

This paper demonstrates that a bulk scalar field in a Randall-Sundrum braneworld can effectively mimic 4D inflaton dynamics, with late-time behavior dominated by specific Green function poles and an effective mass reduction.

Contribution

It shows that bulk scalar field inflation in braneworlds can be described by an effective 4D scalar field with scaled potential, bridging higher-dimensional models with standard cosmology.

Findings

Late-time behavior dominated by Green function poles

Effective 4D scalar field with mass m^2/2 approximates bulk dynamics

Inflation scenario aligns with standard 4D cosmology

Abstract

Based on the recently proposed scenario of inflation driven by a bulk scalar field in the braneworld of the Randall-Sundrum (RS) type, we investigate the dynamics of a bulk scalar field on the inflating braneworld. We derive the late time behavior of the bulk scalar field by analyzing the property of the retarded Green function. We find that the late time behavior is basically dominated by a single (or a pair of) pole(s) in the Green function irrespective of the initial condition and of the signature of $m^{2}=V''(\phi)$, where $V(\phi)$ is the potential of the bulk scalar field. Including the lowest order back-reaction to the geometry, this late time behavior can be well approximated by an effective 4-dimensional scalar field with $m^2_{\mathrm{eff}}=m^2/2$. The mapping to the 4-dimensional effective theory is given by a simple scaling of the potential with a redefinition of the field. Our result supports the picture that the scenario of inflation driven by a bulk scalar field works in a quite similar way to that in the standard 4-dimensional cosmology.