Radion dynamics, heavy Kaluza–Klein resonances and gravitational waves

Abstract

In this paper, we study the confinement/deconfinement phase transition of the radion field in a warped model with a polynomial bulk potential. The backreaction of the radion on the metric is taken into account by using the superpotential formalism, while the radion effective potential is obtained from a novel formulation which can incorporate the backreaction. The phase transition leads to a stochastic gravitational wave background that depends on the energy scale of the first Kaluza–Klein resonance, [Formula: see text]. This work completes previous studies in the following aspects: (i) we detail the evaluation of the radion spectrum; (ii) we report on the mismatches between the thick wall approximation and the numerical bounce solution; (iii) we include a suppression factor in the spectrum of sound waves accounting for their finite lifetime; and (iv) we update the bound on [Formula: see text] in view of the O3 LIGO and Virgo data. We find that the forthcoming gravitational wave interferometers can probe scenarios where [Formula: see text], while the O3-run bounds rule out warped models with [Formula: see text] exhibiting an extremely strong confinement/deconfinement phase transition.