[Paper Review] Implication of nano-Hertz stochastic gravitational wave on dynamical dark matter through a dark first-order phase transition

Siyu Jiang, Aidi Yang+2 more|arXiv (Cornell University)|Jun 30, 2023

Cosmology and Gravitation Theories56 references12 citations

TL;DR

The paper links nano-Hertz stochastic gravitational waves from a strong dark sector first-order phase transition to dynamical dark matter scenarios, analyzing Q-ball/Fermi-ball and super-cool DM and showing SGWB spectra can align with NANOGrav data.

ABSTRACT

For the first time, the expected stochastic gravitational wave background is probably discovered after observing the Hellings Downs correlation curve by several pulsar timing array (PTA) collaborations around the globe including NANOGrav, European PTA, Parkes PTA, and Chinese PTA. These new observations can help to explore or constrain the dark matter (DM) formation mechanisms in the early Universe. We study the implication of those results on the dynamical DM formation mechanisms through a dark first-order phase transition in the early Universe. Both the Q-ball DM and super-cool DM are investigated in the strong super-cooling dark phase transition scenario which may give an interpretation of the observed stochastic gravitational wave background.

Motivation & Objective

• Motivate how nano-Hertz SGWB observations constrain dark matter formation in the early universe.
• Investigate dynamical dark matter production mechanisms during a strong dark first-order phase transition.
• Compare Q-ball/Fermi-ball DM and super-cool DM in the context of SGWB signals.
• Provide phase-transition dynamics and penetration-rate calculations to connect DM production with SGWB.
• Evaluate SGWB spectra against NANOGrav observations to identify viable parameter regions.

Proposed method

• Model the dark sector with a conformal scalar field and a dark U(1) gauge interaction to realize a strong super-cooling dark FOPT.
• Compute the finite-temperature effective potential combining Coleman-Weinberg and thermal corrections to determine T_n and T_p.
• Use bubble-wall dynamics and DM penetration rate across the wall to derive R_in as a function of v_w, m_chi, and T.
• Relate DM relic density in Q-ball/Fermi-ball and super-cool DM scenarios to the phase transition parameters and R_in.
• Calculate the SGWB spectrum from bubble collisions, sound waves, and turbulence in the percolation-driven FOPT and compare with NANOGrav data.
• Present benchmark points that reproduce Omega_DM h^2 = 0.12 and show corresponding phase-transition parameters.

Figure 1: The values of nucleation temperature $T_{n}$ and percolation temperature $T_{p}$ as function of the $y_{A}$ . We choose $M=10~{}\mathrm{MeV}$ .

Experimental results

Research questions

• RQ1 How does a strong super-cooling dark FOPT influence the production and relic density of dynamical dark matter (Q-ball, Fermi-ball, and super-cool DM)?
• RQ2 Can nano-Hertz SGWB signals observed by PTAs be explained by SGWB from dark sector phase transitions linked to DM formation?
• RQ3 What are the relationships between phase-transition parameters (T_p, alpha_p, beta/H_p, v_w) and DM penetration dynamics across the bubble wall?
• RQ4 What parameter regions reproduce the observed DM relic density while yielding SGWB spectra compatible with NANOGrav observations?

Key findings

• A strong super-cooling dark FOPT can yield SGWB spectra at nano-Hertz frequencies compatible with NANOGrav observations.
• DM penetration rate across the bubble wall depends on m_χ/T and bubble-wall velocity, with higher v_w increasing penetration and larger m_χ/T suppressing it.
• Q-ball and Fermi-ball DM scenarios arise when DM is trapped or partially penetrates bubbles, with relic densities set by the interplay of R_in, c_χ, and S_3(T_* )/T_*.
• In Fermi-ball DM, the SGWB is dominated by sound waves and can fit the low-frequency NANOGrav signal for benchmark points with specific v_w, y_χ, and c_χ values.
• The super-cool DM mechanism dilutes DM density via inflation and reheating, potentially yielding compatible relic density without requiring standard freeze-out.