Gravitational Waves and Cosmological Observables from First-Order Phase Transitions: Thermal Corrections at Low Temperature

Abstract

We consider the impact on cosmological first-order phase transitions (FOPTs) of low-temperature thermal corrections to the effective potential. These are corrections from degrees of freedom whose field-dependent masses in the true vacuum are much larger than the nucleation temperature, though in the false vacuum the field-dependent masses may be much smaller than the nucleation temperature. Although the general form of these corrections to the thermal effective potential can be quite complicated, we argue that the net effect of all such corrections can be well-modeled with a single new parameter. We determine the shift in the parameters of the FOPT in terms of this new parameter, and the impact on gravitational wave signals and cosmological observables.

Figures (2)

• Figure 1: $V(\tilde{\phi}, \tilde{T}_N)$ for the benchmark point $(b,c) = (-2.69, 9.00)$, for $f = 0, \pm 0.996$, as labeled.
• Figure 2: $T_N$ (in units of $v$, upper left panel), $\beta/H$ (upper middle panel) and $\xi$ (upper right panel), as functions of $f$, for three benchmark choices of $(b,c)$, as labeled. Also shown are the peak values $f_{sw}$ (lower right panel) and $h^2 \Omega_{sw}$ (lower middle panel) as functions of $f$, and $h^2 \Omega_{sw}$ as a function of $f_{sw}$ (lower right panel). The blue dots are obtained from CosmoTransitions, and the dashed blue line is a linear fit to these points. The red star is a prediction from the analytic form of $S_3/T$, and the red dashed line is the analytic fit. Note that, in each case, the blue dot corresponding to $f=0$ lies under the red star.