Vacuum destabilization from Kaluza-Klein modes in an inflating brane

Abstract

We discuss the effects from the Kaluza-Klein modes in the brane world scenario when an interaction between bulk and brane fields is included. We focus on the bulk inflaton model, where a bulk field $Ψ$ drives inflation in an almost $AdS_5$ bulk bounded by an inflating brane. We couple $Ψ$ to a brane scalar field $ϕ$ representing matter on the brane. The bulk field $Ψ$ is assumed to have a light mode, whose mass depends on the expectation value of $ϕ$. To estimate the effects from the KK modes, we compute the 1-loop effective potential $V_\eff(ϕ)$. With no tuning of the parameters of the model, the vacuum becomes (meta)stable -- $V_\eff(ϕ)$ develops a true vacuum at a nonzero $ϕ$. In the true vacuum, the light mode of $Ψ$ becomes heavy, degenerates with the KK modes and decays. We comment on some implications for the bulk inflaton model. Also, we clarify some aspects of the renormalization procedure in the thin wall approximation, and show that the fluctuations in the bulk and on the brane are closely related.