Study of gravitational waves from phase transitions in three-component dark matter

TL;DR

The paper investigates gravitational waves from a strong first-order electroweak phase transition in a three-component dark-matter model that includes a scalar mediator $\phi$ and a dark $U_D(1)$ gauge sector. It constructs the Lagrangian, applies the Gildener-Weinberg flat-direction mechanism, and computes the one-loop finite-temperature effective potential with daisy resummation to obtain $T_c$, $T_n$, and $T_p$, using the Euclidean action (via AnyBubble) to determine bubble dynamics. For nine Planck-consistent benchmarks, it evaluates the GW spectrum from bubble collisions, sound waves, and turbulence, finding that the peak signal lies near $f\sim 10^{-3}$ Hz and that the amplitude increases with the strength parameter $\alpha$ while decreasing with $\beta/H_*$. The results indicate that LISA is unlikely to detect these backgrounds, but future detectors like BBO and μAres could probe substantial portions of the predicted spectra, offering a complementary test of this DM framework and its direct-detection implications.

Abstract

This paper studies gravitational waves in a dark matter model composed of three types of particles with distinct spins, along with a scalar field $φ$ that mediates interactions between Standard Model particles and dark matter. It discusses the electroweak phase transition following the Big Bang, during which all particles are initially massless due to the inactive Higgs mechanism. As temperature decreases, the effective potential reaches zero at two points, leading to two minima at the critical temperature ($T_c$), and eventually to a true vacuum state. The formation of new vacuum bubbles, where electroweak symmetry is broken and particles acquire mass, generates gravitational waves as these bubbles interact with the fabric of space-time. The paper derives the gravitational wave frequency and detection range based on the model's parameters, aligning with observational data from the Planck satellite and detection thresholds from PandaX-4T and XENONnT for some parameter points. It concludes by comparing the predicted background gravitational wave density with the sensitivities of LISA, BBO and $μ$-Ares detectors.

Figures (7)

• Figure 1: The relative positions of the Higgs and scalar fields as indicated in (\ref{['rotationMatrix']}).
• Figure 2: These figures illustrate the points from table \ref{['tableOmega']} in relation to rescaled DM-Proton cross section versus DM masses, with $\nu_2$ and relic density ${\Omega}h^2$ represented by color bar.
• Figure 3: The blue line shows $S_3(T)/T$ as a function of T, while the dashed red and purple lines indicate the values $S_3(T)/T=140$ and $S_3(T)/T=100$, respectively, at which nucleation and percolation occur. The black dots are derived using the AnyBubble package.
• Figure 4: Effective potential diagrams of points in table \ref{['tableTC']} as a function of $\phi$ scalar field at percolation ,nucleation, critical, and supercritical temperatures.
• Figure 5: GW spectrum as a function of backgound gravitational frequency for points in Table \ref{['tableBetaH']}, considering $v_w=1$.