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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, m 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 KK in view of the O3 LIGO and Virgo data. We find that the forthcoming gravitational wave interferometers can probe scenarios where m KK ≲ 1 0 9 TeV , while the O3-run bounds rule out warped models with 1 0 4 TeV ≲ m KK ≲ 1 0 7 TeV exhibiting an extremely strong confinement/deconfinement phase transition. [ABSTRACT FROM AUTHOR]

Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the ∼ 10 –103 Hz band of ground-based observatories and the ∼ 1 0 − 4 –10− 1 Hz band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass (∼ 1 0 2 –104M⊙) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology. [ABSTRACT FROM AUTHOR]