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Diluting the Dark Sector: A Common Origin for the PTA Signal and Inelastic SIDM

Zihan Wang

TL;DR

The paper tackles the amplitude tension in the nanohertz SGWB reported by NANOGrav, proposing the Radiative SIDM Dilution framework that unifies a dark-sector phase transition with SIDM-driven suppression of astrophysical GW backgrounds. It analyzes a scalar-mediated inelastic SIDM model with gauged $U(1)_D$, where a strong first-order phase transition at $T_* \approx 1.24$ MeV (with $\alpha \approx 465$ and $\beta/H_* \approx 150$) generates a cosmological GW peak, while entropy release dilutes the DM relic density by $D \approx 100$ and leaves a residual dark radiation component of $\Delta N_{\rm eff} \approx 0.3$. The model naturally links the GW amplitude to the DM abundance, via reheating to $T_{rh} \approx 5.76$ MeV, and predicts a present-day primordial magnetic field seed of $B_0 \sim 10^{-13}$ G through MHD turbulence and helicity. Bayesian model comparison favors the Hybrid scenario (stalled astrophysical floor plus a phase-transition GW) over purely standard interpretations with $\Delta\text{BIC} \approx 15$, offering a falsifiable, multi-faceted cosmological framework with observable consequences including inelastic nuclear scattering signatures in future detectors.

Abstract

The recent detection of a nanohertz stochastic gravitational wave background (SGWB) challenges conventional astrophysics by observed signal amplitude exceeds predictions from standard SMBHB populations without implausible accretion histories. To resolve this amplitude tension, we introduce the Radiative SIDM Dilution framework.We explain the observed spectrum emerges as a hybrid signal by an astrophysical floor, dynamically suppressed by the cored halos of Self-Interacting Dark Matter (SIDM),and a dominant cosmological peak generated during a supercooled phase transition in the dark sector. By performing a free spectral reconstruction and Bayesian model comparison, we demonstrate that a transition defined by a nucleation temperature $T_* \approx 1.24$ MeV and inverse duration $β/H_* \approx 150$ not only fills the spectral gap left by stalled binaries but yields statistical evidence($Δ\text{BIC} \approx 15$) over purely standard astrophysical interpretations. The thermodynamics required to reproduce this SGWB signature also resolves the thermal overproduction of resonant SIDM. The entropy injected by the transition naturally provides the specific dilution factor $D \approx 100$ needed to reset the dark matter relic density to observation. This mechanism also has broader cosmological consequences.The residual dark radiation alleviates the Hubble tension $ΔN_{\rm eff} \sim 0.3$ while bubble collisions generate magnetohydrodynamic turbulence sufficient to seed primordial magnetic fields $B_0 \sim 10^{-13}$ G. These convergences suggest that the NANOGrav excess is not an anomaly, but the acoustic signature of the entropy injection event that rendered the dark sector cosmologically viable.

Diluting the Dark Sector: A Common Origin for the PTA Signal and Inelastic SIDM

TL;DR

The paper tackles the amplitude tension in the nanohertz SGWB reported by NANOGrav, proposing the Radiative SIDM Dilution framework that unifies a dark-sector phase transition with SIDM-driven suppression of astrophysical GW backgrounds. It analyzes a scalar-mediated inelastic SIDM model with gauged , where a strong first-order phase transition at MeV (with and ) generates a cosmological GW peak, while entropy release dilutes the DM relic density by and leaves a residual dark radiation component of . The model naturally links the GW amplitude to the DM abundance, via reheating to MeV, and predicts a present-day primordial magnetic field seed of G through MHD turbulence and helicity. Bayesian model comparison favors the Hybrid scenario (stalled astrophysical floor plus a phase-transition GW) over purely standard interpretations with , offering a falsifiable, multi-faceted cosmological framework with observable consequences including inelastic nuclear scattering signatures in future detectors.

Abstract

The recent detection of a nanohertz stochastic gravitational wave background (SGWB) challenges conventional astrophysics by observed signal amplitude exceeds predictions from standard SMBHB populations without implausible accretion histories. To resolve this amplitude tension, we introduce the Radiative SIDM Dilution framework.We explain the observed spectrum emerges as a hybrid signal by an astrophysical floor, dynamically suppressed by the cored halos of Self-Interacting Dark Matter (SIDM),and a dominant cosmological peak generated during a supercooled phase transition in the dark sector. By performing a free spectral reconstruction and Bayesian model comparison, we demonstrate that a transition defined by a nucleation temperature MeV and inverse duration not only fills the spectral gap left by stalled binaries but yields statistical evidence() over purely standard astrophysical interpretations. The thermodynamics required to reproduce this SGWB signature also resolves the thermal overproduction of resonant SIDM. The entropy injected by the transition naturally provides the specific dilution factor needed to reset the dark matter relic density to observation. This mechanism also has broader cosmological consequences.The residual dark radiation alleviates the Hubble tension while bubble collisions generate magnetohydrodynamic turbulence sufficient to seed primordial magnetic fields G. These convergences suggest that the NANOGrav excess is not an anomaly, but the acoustic signature of the entropy injection event that rendered the dark sector cosmologically viable.
Paper Structure (44 sections, 60 equations, 2 figures)

This paper contains 44 sections, 60 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Particle Physics Model
  3. Phase Transition Dynamics
  4. Experimental Viability
  5. Dark Matter Genesis Mechanism
  6. The Overproduction Crisis
  7. Entropic Unification
  8. Gravitational Wave Analysis
  9. Phase Transition Signal
  10. Bayesian Model Selection and Spectral Curvature
  11. The Astrophysical Floor and SIDM Effects
  12. Cosmological Implications
  13. Hubble Tension and Dark Sector Decay
  14. Primordial Magnetic Fields
  15. Global Robustness of the Unified Solution
  16. ...and 29 more sections

Figures (2)

  • Figure 1: The gray violins represent the full posterior probability density of the NANOGrav 15-year free spectrum at each frequency bin.The Standard Astrophysical Model (blue dashed, $\gamma=13/3$) fails to capture the high-frequency spectral curvature, effectively slicing through the low-probability tails. The Hybrid Dark Sector Model (red solid) provides a superior geometric fit, rising as $f^3$ to match the "dome" at $f \sim 10-20$ nHz before decaying. This model combines a stalled astrophysical floor with a phase transition signal ($T_* \approx 1.24$ MeV, $\alpha \approx 465$), yielding a $\Delta \text{BIC} \approx 15$ preference over the standard scenario.
  • Figure 2: Robustness of the radiative SIDM dilution. A global parameter scan in the ($\alpha$, $\beta/H_*$) plane illustrating the joint fit to three cosmological observables. Blue dashed contours indicate the peak gravitational wave amplitude $\Omega_{GW}h^2$ (including finite duration suppression), matching the NANOGrav 15-year signal region ($\sim 10^{-9}$). Red dotted contours show the entropy dilution factor $D$, which is analytically tied to the transition strength ($D \approx \alpha^{3/4}$). The benchmark point ($T_*=1.24$ MeV, $\alpha \approx 465$, $\beta/H_* \approx 150$) sits within the optimal region where the dilution ($D \approx 100$) solves the SIDM relic density problem and the residual dark radiation ($\Delta N_{eff} \approx 0.3$) alleviates the Hubble tension.