Radion dynamics, heavy Kaluza-Klein resonances and gravitational waves

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, $m_{\text{KK}}$. 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 $m_{\text{KK}}$ in view of the O3 LIGO and Virgo data. We find that the forthcoming gravitational wave interferometers can probe scenarios where $m_{\text{KK}}\lesssim {10}^9$ TeV, while the O3-run bounds rule out warped models with $10^4 $\text{TeV}$ \lesssim m_{$\text{KK}$} \lesssim 10^7$ TeV exhibiting an extremely strong confinement/deconfinement phase transition.