Cosmological Phase Transitions in Warped Space: Gravitational Waves and Collider Signatures

TL;DR

This work develops a generalized superpotential framework to study cosmological phase transitions in 5D warped soft-wall models with strong IR back-reaction. It demonstrates that a holographic (radion/dilaton) phase transition can be first order and produce a detectable stochastic gravitational-wave background, while predicting heavy radion signatures potentially observable at future colliders. The analysis reveals that, depending on back-reaction, the electroweak phase transition can be sequential or simultaneous with the radion transition, with reheating temperatures ranging from TeV to near EW scales and implications for electroweak baryogenesis. Overall, the study links holographic phase-transition dynamics to GW astronomy and collider phenomenology, offering a coherent, testable picture in next-generation experiments.

Abstract

We study the electroweak phase transition within a 5D warped model including a scalar potential with an exponential behavior, and strong back-reaction over the metric, in the infrared. By means of a novel treatment of the superpotential formalism, we explore parameter regions that were previously inaccessible. We find that for large enough values of the t'Hooft parameter (e.g. $N\simeq 25$) the holographic phase transition occurs, and it can force the Higgs to undergo a first order electroweak phase transition, suitable for electroweak baryogenesis. The model exhibits gravitational waves and colliders signatures. It typically predicts a stochastic gravitational wave background observable both at the Laser Interferometer Space Antenna and at the Einstein Telescope. Moreover the radion tends to be heavy enough such that it evades current constraints, but may show up in future LHC runs.

Figures (8)

• Figure 1: Left panels: Effective potential for different values of $\lambda_1$ in units of $\ell$. Only the relevant regime $r_1>\langle r_1 \rangle$ is considered. Right panels: The relative correction to the superpotential $sW_1(v_1)/W_0(v_1)$ as a function of $r_1$. The panels on the top correspond to 'small back-reaction scenario (class A)', while the panels on the bottom correspond to 'large back-reaction scenario (class B)'.
• Figure 2: The effective potential as a function of $\mu$, in units of $\ell$, in scenarios A$_1$, B$_8$, C$_2$, $E_1$ (left panel) and D$_1$ (right panel).
• Figure 3: The quantities $a_h(T)$ (blue solid line) and $\kappa^2F_{\rm min}/(\pi^4\ell^3T^4)$ (red dashed line) as a function of $T$ in the scenarios of the class A (left panel) and class B (right panel).
• Figure 4: $\mu_0$ (left panel) and $S_4$ and $S_3/T$ (right panel) as a function of the temperature in the benchmark scenario A$_1$ where the back-reaction is small. Dimensional quantities are in units of $\langle \mu \rangle$ with values quoted in Tab. \ref{['tab:table']}.
• Figure 5: Upper panels: As in Fig. \ref{['fig:S3S4Small']} but for scenario B$_8$. Lower panels: As in Fig. \ref{['fig:S3S4Small']} but for scenario B$_2$. The findings are qualitatively similar to those arising in the most common parameter scenarios where the back-reaction is large (cf. Fig. \ref{['fig:S3S4smallkappa']}).