Radion dynamics, heavy Kaluza–Klein resonances and gravitational waves

We study the confinement/deconfinement phase transition of radion field in a warped model with polynomial bulk potential. The backreaction on metric is taken into account by using superpotential formalism, while effective potential obtained from novel formulation which can incorporate backreaction. leads to stochastic gravitational wave background that depends energy scale first Kaluza-Klein resonance, $m_{\textrm{KK}}$. This work completes previous studies following aspects: i) we detail evaluation spectrum; ii) report mismatches between thick wall approximation and numerical bounce solution; iii) include suppression factor spectrum sound waves accounting for their finite lifetime; and, iv) update bound $m_{\textrm{KK}}$ view O3 LIGO Virgo data. find forthcoming interferometers probe scenarios where $m_{\textrm{KK}} \lesssim 10^9$ TeV, O3-run bounds rule out models $10^4 \textrm{TeV} m_{\textrm{KK}} 10^7$ TeV exhibiting an extremely strong transition.