Supercooled Dark Scalar Phase Transitions explanation of NANOGrav data

TL;DR

This work tackles the NANOGrav PTA SGWB by proposing a minimal dark-sector scenario with a U(1)_D gauge group and a dark scalar that undergoes a supercooled first-order phase transition at the 100 MeV–GeV scale. It advances beyond common approximations by computing a fully consistent finite-temperature one-loop effective potential, tracking percolation and completion without relying on the bag model and by using the mean bubble separation R_* to derive the GW spectrum. The analysis shows that, with g_D near the zero-temperature barrier threshold g_D^{roll} and a small λ_φ, the FOPT can complete and produce a sound-wave–dominated GW signal compatible with NANOGrav data, predicting a heavier dark gauge boson relative to the dark scalar. This links early-Universe microphysics in a dark sector to observable SGWB features and guides future laboratory probes of dark sectors.

Abstract

The evidence of a Stochastic Gravitational Wave Background (SGWB) in the nHz frequency range is posed to open a new window on the Universe. A preferred explanation relies on a supercooled first order phase transition at the 100 MeV - GeV scale. In this article, we address the feasibility going from the particle physics model to the production of the gravitational waves. We take a minimal approach for the dark sector model introducing the fewest ingredients required, namely a new U(1) gauge group and a dark scalar that dynamically breaks the symmetry. Supercooling poses challenges in the analysis that put under question the feasibility of this explanation: we address them, going beyond previous studies by carefully considering the effects of a vacuum domination phase and explicitly tracking the phase transition from its onset to its completion. We find that the proposed model can successfully give origin to the observed PTA SGWB signal. The strong supercooling imposes a correlation between the new gauge coupling and the scalar quartic one, leading to a significant hierarchy between the (heavier) gauge boson and the dark scalar. Ultimately, information on phase transitions from SGWB observations could provide a direct probe of the microphysics of the Early Universe and be used to guide future searches of dark sector in laboratories.

Figures (3)

• Figure 1: Gravitational wave spectrum for the reference points in Table \ref{['tab:benchmarks']}. The gray shaded regions correspond to NANOGrav's violin plot.
• Figure 2: Upper panel: Maximum (minimum) value $g_\mathrm{max}$ ($g_\mathrm{min}$) of the gauge coupling for which a FOPT completes as a function of the scalar quartic coupling $\lambda_{\phi}$, shown in dark red (blue). The dashed line corresponds to the values for which a potential barrier is present at zero temperature (see Eq. (\ref{['eq:g_roll']})). Lower panel: Values of the different relevant temperatures as a function of $\lambda_{\phi}$ for $g_D=g_D^{\mathrm{max}}$. In both panels the vev is fixed to that of BP2 and BP4 in Table \ref{['tab:benchmarks']}.
• Figure 3: Evolution of the false vacuum fraction of the Universe $\mathcal{P}_f$ as a function of the temperature, shown in dark red. The dark green, teal and purple dash-dotted vertical lines correspond to the nucleation, percolation and completion temperatures, respectively. The horizontal coral and light-green dashed lines correspond to the values of $\mathcal{P}_f(T)$ that define the percolation and completion temperatures, respectively. The left panel corresponds to a point in which the FOPT does not complete, while the right one is BP2 in Table \ref{['tab:benchmarks']}.