Gravitational Waves from First-Order Phase Transitions Assisted by Temperature-Enhanced Scatterings

Abstract

Scatterings whose cross sections increase as the cosmic temperature decreases, known as temperature - enhanced scatterings, can have a significant impact on the thermal effective potential of scalar fields responsible for driving cosmological first-order phase transitions. We show that such effects naturally manifest as finite-temperature self-energy corrections to the scalar mass term, leading to an additional contribution of the form \(c\,T^{p}φ^{2}\) in the effective potential. In this work, we systematically investigate how these loop-induced, temperature-dependent corrections affect key phase transition parameters, including the nucleation temperature, latent heat release, and inverse duration parameter. These modifications influence both the strength and duration of the phase transition, which in turn determine the properties of the resulting stochastic gravitational-wave (GW) background. Employing semi-analytic computational methods, we evaluate the GW spectra generated under these conditions and compare our predictions with the projected sensitivities of forthcoming detectors such as LISA, DECIGO, and BBO. Our analysis demonstrates that finite-temperature scattering effects of this kind can substantially strengthen first-order transitions and produce GW signals that lie within the reach of future observational facilities. The results establish a concrete thermal-field-theoretic origin for temperature-dependent modifications of the scalar potential and emphasize their importance in shaping early-Universe cosmological signatures.

Figures (8)

• Figure 1: Evolution of the effective potential $V_{\mathrm{eff}}(\phi,T)$ as the Universe cools, shown at several temperatures $T$. Solid lines include the temperature-enhanced scattering term $c T^p \phi^2$, while dashed lines show the standard potential without this term. The new term deepens the broken phase minimum or delays the transition, illustrating how temperature-enhanced scatterings can impact the dynamics of the phase transition.
• Figure 2: Temperature dependence of the bounce action $S_3(T)/T$ for different exponents $p$ in the temperature-enhanced scattering term. The horizontal dashed line at $S_3/T=140$ indicates the nucleation criterion. Red points mark the nucleation temperature $T_n$ where the bounce action drops below this threshold. The temperature on the x-axis is shown in units of the critical temperature, $T/T_c$, making the plot dimensionless. As $p$ varies, the dynamics of the phase transition change, shifting the nucleation temperature and affecting the strength and duration of the transition.
• Figure 3: Scan over the temperature-enhanced scattering parameters $p$ and $c$. Left: Strength parameter $\alpha$. Right: Inverse duration parameter $\beta/H$. Regions with larger $\alpha$ and smaller $\beta/H$ correspond to stronger and longer-lasting phase transitions, most pronounced for large negative $p$ and moderate $c$.
• Figure 4: Nucleation temperature $T_n$ normalized to the critical temperature $T_c$ versus exponent $p$ for different values of $c$. Larger negative $p$ leads to later nucleation (lower $T_n/T_c$), as the scattering term increasingly favors the broken phase at lower temperatures.
• Figure 5: Correlation between the strength parameter $\alpha$ and inverse duration parameter $\beta/H$ across the scanned parameter space. Temperature-enhanced scatterings extend the region of strong and slow transitions (upper-left region), enhancing the predicted GW signal.