Impact of Supercooling on Direct Searches for Dark Matter and Gravitational Wave Backgrounds

TL;DR

The paper investigates how a supercooled first-order phase transition in the early universe modifies dark matter production and the associated gravitational-wave background. It develops a modified Boltzmann framework for freeze-out during supercooling (with a constant Hubble rate) and analyzes freeze-in under non-standard expansion, including the entropy dilution from reheating. Through benchmark scenarios such as a supercooled electroweak transition and millicharged dark matter in a dark QED setup, it shows that WIMP-like DM can become viable in regions previously excluded and that freeze-in predictions can move closer to experimental reach. The work highlights a complementary link between direct detection prospects and low-frequency gravitational-wave signals as signatures of early-universe supercooling dynamics.

Abstract

An interesting feature of a cosmological phase transition can be a stage of exponential expansion (supercooling). The modified expansion history and the entropy injection at reheating, can affect the final energy fraction of dark matter. In this paper, we revisit the calculation of the freeze-out and freeze-in dynamics, showing additional effects on top of the standard dilution factor if the dark matter production is completed during the supercooling stage. We show for the first time how these effects can be particularly interesting for direct detection, as the parameter space for WIMP-like candidates shifts from excluded to allowed regions, and freeze-in candidates get closer to experimental reach. A phenomenological motivation to consider supercooling is the associated gravitational wave background. The implications of a finite-duration reheating stage, when the equation of state is close to matter-domination, are a peculiar low-frequency spectrum, and its shift to lower frequencies. These effects are a complementary test of the dynamics that we study for dark matter production, and remarkably can link direct detection of dark matter and gravitational wave astronomy.

Figures (9)

• Figure 1: Schematic evolution of the energy density in the Universe around a supercooled phase transition, and impact on the production of dark matter in a separate sector. In this paper, we focus on the implications for direct detection of dark matter candidates whose abundance is set around the supercooled PT via freeze-out or freeze-in. We show how a supercooling stage can enhance the chances of detection at direct searches, and we conclude by discussing the gravitational wave background produced at the end of supercooling, and the signature of the reheating stage on the low-frequency causality tail.
• Figure 2: DM freeze-out for several masses. The plotted yield $Y$ is evaluated before the end of supercooling and the consequent entropy injection, that dilutes $Y$ by a factor $(T_\text{nuc}/T_\text{inf})^3$. The solid lines are the full solution to the Boltzmann equation while the circular dots indicate the moment where $\Delta Y(x)/Y_{\text{EQ}}(x)=2$, that we identify as freeze-out condition. For comparison, we show as dashed lines the solution that one would get for same mass and cross section in a standard radiation dominated universe. The vertical line describes the onset of supercooling while $\Delta N$ is the number of $e$-folds elapsed since that moment. In these plots $T_\text{inf} =120\, \textrm{GeV}$ and $\sigma=10^{-11}m_{\textsc{dm}}^{-2}$.
• Figure 3: The solid blue lines show the required supercooling as a function of DM masses for several annihilation cross sections $\sigma$, ranging from $\sigma=10^{-13} m_{\textsc{dm}}^{-2}$ to $\sigma=10^{-10} m_{\textsc{dm}}^{-2}$. We fix here $T_\textsc{rh}=0.05\,T_\text{inf}$. The dashed lines represent the results that we would obtain by considering a radiation-dominated universe. In purple, we show the analytic approximation of \ref{['eq:hotRelic']}.
• Figure 4: Constraints from direct detection experiments on the spin-independent dark matter–nucleon cross section as a function of the dark matter mass, including results from LZ LZ:2024zvo, XENONnT XENON:2025vwd, PandaX PandaX:2024qfu, DarkSide-50 DarkSide-50:2022qzh, and CRESST CRESST:2019jnq. The red triangles and yellow stars indicate the points that yield the correct relic abundance considering, respectively, just the naive dilution factor or solving the full numerical freeze-out during supercooling. The blue marker indicates the dark matter mass required in the absence of supercooling for this model. Neutrino fog defined according to OHare:2021utq.
• Figure 5: Same as \ref{['fig:DirectSearch']}, considering now DM candidates with masses and couplings fulfilling the standard "WIMP miracle" and a short period of supercooling.