Radion dynamics, heavy Kaluza–Klein resonances and gravitational waves

Abstract

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 back-reaction. The phase transition leads to a stochastic gravitational wave background that depends on the energy scale of the first Kaluza-Klein resonance, mKK. 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 mKK in view of the O3 LIGO and Virgo data. We find that the forthcoming gravitational wave interferometers can probe scenarios where mKK less than or similar to 10(9) TeV, while the O3-run bounds rule out warped models with 10(4) TeV less than or similar to mKK less than or similar to 10(7) TeV exhibiting an extremely strong confinement/deconfinement phase transition.