Models with radiative symmetry breaking typically feature strongly supercooled first-order phase transitions, which result in an observable stochastic gravitational wave background. In this work, we analyse the role of higher-order thermal corrections for these transitions, applying high-temperature dimensional reduction to a theory with dimensional transmutation. In particular, we study to what extent high-temperature effective field theories (3D EFT) can be used. We find that despite significant supercooling down from the critical temperature, the high-temperature expansion for the bubble nucleation rate can be applied using the 3D EFT framework, and we point out challenges in the EFT description. We compare our findings to previous studies and find that the next-to-leading order corrections obtained in this work have a significant effect on the predictions for GW observables, motivating a further exploration of higher-order thermal effects.

WallGo is an open-source software designed to compute the bubble wall velocity in first-order cosmological phase transitions. Additionally, it evaluates the energy budget available for generating gravitational waves. The main part of WallGo, built in Python, determines the wall velocity by solving the scalar-field(s) equation of motion, the Boltzmann equations and energy-momentum conservation for the fluid velocity and temperature. WallGo also includes two auxiliary modules: WallGoMatrix, which computes matrix elements for out-of-equilibrium particles, and WallGoCollision, which performs higher-dimensional integrals for Boltzmann collision terms. Users can implement custom models by defining an effective potential and specifying a list of out-of-equilibrium particles and their interactions. As the first public software to compute the wall velocity including out-of-equilibrium contributions, WallGo improves the precision of the computation compared to common assumptions in earlier computations. It utilises a spectral method for the deviation from equilibrium and collision terms that provides exponential convergence in basis polynomials, and supports multiple out-of-equilibrium particles, allowing for Boltzmann mixing terms. WallGo is tailored for non-runaway wall scenarios where leading-order coupling effects dominate friction. While this work introduces the software and the underlying theory, a more detailed documentation can be found in https://wallgo.readthedocs.io.

We point out that a model with scalar fields with a large nonminimal coupling to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear sigma model (NLSM). With the inclusion of not only the scalar fields but also the conformal mode of the metric, our definition of the target space of the NLSM is invariant under the frame transformation. We show that theσ-meson that linearizes this NLSM to be a linear sigma model (LSM) corresponds to the scalaron, the degree of freedom associated to theR²term in the Jordan frame. We demonstrate that quantum corrections inevitably induce thisσ-meson in the large-Nlimit, thus providing a frame independent picture for the emergence of the scalaron. The resultant LSM only involves renormalizable interactions and hence its perturbative unitarity holds up to the Planck scale unless it hits a Landau pole, which is in agreement with the renormalizability of quadratic gravity.

We have conducted extensive lattice simulations to study the postinflation dynamics of multifield models involving nonminimal couplings. We explore the parameter dependence of preheating in these models and describe the various time scales that control such nonlinear processes as energy transfer, rescattering, and the approach to radiation domination and thermalization. In the limit of large nonminimal couplings (${\xi }_I\sim 100$), we find that efficient transfer of energy from the inflaton condensate to radiative degrees of freedom, emergence of a radiation-dominated equation of state, and the onset of thermalization each consistently occur within $N_{\mathrm{reh}}\lesssim 3$ $e$-folds after the end of inflation, largely independent of the values of the other couplings in the models. The exception is the case of negative ellipticity, in which there is a misalignment between the dominant direction in field space along which the system evolves and the larger of the nonminimal couplings ${\xi }_I$. In those cases, the field-space-driven parametric resonance is effectively shut off. More generally, the competition between the scalar fields’ potential and the field-space manifold structure can yield interesting phenomena such as two-stage resonances. Across many regions of parameter space, we find efficient re-scattering between the distinct fields, leading to a partial memory loss of the shape of the initial fluctuation spectrum. Despite the explosive particle production, which can lead to a quick depletion of the background energy density, the nonlinear processes do not induce any superhorizon correlations after the end of inflation in these models, which keeps predictions for cosmic microwave background observables unaffected by the late-time amplification of isocurvature fluctuations. Hence the excellent agreement between primordial observables and recent observations is preserved for this class of models, even when we consider postinflation dynamics.

The energy budget for gravitational waves of a cosmological first order phase transitions depends on the speed of sound in the thermal plasma in both phases around the bubble wall. Working in the real-singlet augmented Standard Model, which admits a strong two-step electroweak phase transition, we compute higher order corrections to the pressure and sound speed. We compare our result to lower-order approximations to the sound speed and the energy budget and investigate the impact on the gravitational wave signal. We find that deviations in the speed of sound from $$ {c}_s^2 $$c s 2 = 1/3 are enhanced up to $$ \mathcal{O} $$O (5%) in our higher-order computation. This results in a suppression in the energy budget of up to $$ \mathcal{O} $$O (50%) compared to approximations assuming $$ {c}_s^2 $$c s 2 = 1/3. The effect is most significant for hybrid and detonation solutions. We generalise our discussion to the case of multiple inert scalars and the case of a reduced number of fermion families in order to mimic hypothetical dark sector phase transitions. In this sector with modified field content, the sound speed can receive significant suppression, with potential order-of-magnitude impact on the gravitational wave amplitude.