  Thermal corrections in classically conformal models typically induce a strong
first-order electroweak phase transition, thereby resulting in a stochastic
gravitational wave background that could be detectable at gravitational wave
observatories. After reviewing the basics of classically conformal scenarios,
in this paper we investigate the phase transition dynamics in a thermal
environment and the related gravitational wave phenomenology within the
framework of scalar conformal extensions of the Standard Model. We find that
minimal extensions involving only one additional scalar field struggle to
reproduce the correct phase transition dynamics once thermal corrections are
accounted for. Next-to-minimal models, instead, yield the desired electroweak
symmetry breaking and typically result in a very strong gravitational wave
signal.
