Inverse bubbles from broken supersymmetry

Abstract

Building upon the recent findings regarding inverse phase transitions in the early universe, we present the first natural realisation of this phenomenon within a supersymmetry-breaking sector. We demonstrate that inverse hydrodynamics, which is characterized by the fluid being aspirated by the bubble wall rather than being pushed or dragged, is actually not limited to a phase of (re)heating but can also occur within the standard cooling cosmology. Through a numerical analysis of the phase transition, we establish a simple and generic criterion to determine its hydrodynamics based on the generalised pseudo-trace. Our results provide a proof of principle highlighting the need to account for these new fluid solutions when considering cosmological phase transitions and their phenomenological implications.

Figures (6)

• Figure 1: Possible solutions to the fluid matching conditions for $(v_-, v_+)$ for the $R$--symmetry breaking FOPT under consideration, plotting the relevant branches for different values of $T_+$ between $T_c$ and the temperature where the barrier disappears. Dashed lines correspond to direct phase transitions, while solid lines indicate inverse transitions, as determined by the sign of $\alpha_\vartheta$. The solid red line highlights the relevant branch at $T_{\text{nuc}}$. The red-shaded area marks the region of strong (inverse) detonations and strong (inverse) deflagrations. In the bottom right corner, a zoomed-in view of the hybrid solution region reveals an overlap between different branches (see Appendix \ref{['app:hydro']} for more details).
• Figure 2: The nucleation temperature (red line) is obtained as a function of $\lambda$ by numerically solving the condition $S_3/T = 140$, which corresponds to setting $\sqrt{F} \sim$ TeV for concreteness (see App. \ref{['app:dynamics']}). The blue-shaded (white) region indicates the occurrence of the inverse (direct) FOPTs, whose boundary is shown according to the criteria $D\vartheta = 0$ and $D\theta = 0$. For this figure we fixed $m/\sqrt{F} = 2$.
• Figure 3: Free energy of the system at finite temperature evaluated at one--loop at the nucleation temperature, with the arrow indicating the direction of the phase transition towards the minimum with a non--zero $x$ (left panel), together with a sketch of the expanding bubble and its velocity in red, and the fluid profile in green (central panel) for a characteristic inverse detonation. The actual fluid profile in the plasma frame is shown in the right panel. Due to its inverse nature, the fluid velocity is always negative. See main text and Appendix \ref{['app:hydro']} for details.
• Figure 4: Dashed (solid) lines represent direct (inverse) phase transitions. The inverse branches emerge as soon as $\alpha_\theta < 0$, whereas this is not necessarily the case for $\alpha_+$. The two strength parameters of the phase transition, $\alpha_+$ and $\alpha_\theta$, coincide in the bag model when $\mu = \nu = 4$.
• Figure 5: Overlap of direct and inverse branches in the $(v_-, v_+)$ plane and corresponding fluid profiles. Left panel: The $(v_-, v_+)$ trajectories for different values of $T_+$. The inverse branch is shown in orange, while the direct branch is displayed in blue. The highlighted crossing point indicates a case where both a direct and an inverse solution exist for the same $(v_-, v_+)$ pair. Middle panel: Fluid profile corresponding to the direct hybrid solution. Right panel: Fluid profile for the inverse hybrid solution. The shaded regions indicate the interior of the bubble.