[Paper Review] Self-interacting dark matter implied by nano-Hertz gravitational waves

Chengcheng Han, Ke-Pan Xie+2 more|arXiv (Cornell University)|Jun 29, 2023

Advanced Thermodynamics and Statistical MechanicsPhysics and Astronomy19 citations

TL;DR

The paper presents a SIDM model where a MeV-scale dark mediator arises from spontaneous breaking of a new U(1)' gauge symmetry during a first-order phase transition, explaining both small-scale structure and nano-Hertz GW signals observed by PTAs.

ABSTRACT

The self-interacting dark matter (SIDM) paradigm offers a potential solution to the small-scale structure problems faced by collision-less cold dark matter. This framework incorporates self-interactions among dark matter particles, typically mediated by a particle with a MeV-scale mass. Recent evidences of nano-Hertz gravitational waves from pulsar timing arrays (PTAs) such as NANOGrav, CPTA, EPTA, and PPTA suggest the occurrence of a first-order phase transition (FOPT) at a MeV-scale temperature. Considering the close proximity between these two scales, we propose that the mediator mass in the SIDM model originates from the spontaneous breaking of a $U(1)'$ symmetry, which is driven by the FOPT indicated by PTA data. Consequently, the alignment of these two scales is believed to be deeply connected by the same underlying physics. By extensively exploring the parameter space, remarkably, we find that the parameter space favored by SIDM just provides an explanation for the PTA data.

Motivation & Objective

• Motivate SIDM as a solution to small-scale structure problems in the CDM paradigm.
• Link the MeV-scale dark mediator to a first-order phase transition suggested by PTA data.
• Show that a unified dark-sector mechanism can account for both SIDM phenomenology and stochastic GWs.
• Identify viable parameter space that satisfies both DM self-interaction and gravitational wave observations.
• Propose experimental probes that can test the model in near-future colliders and direct detection experiments.

Proposed method

• Construct a SIDM framework with a Dirac DM candidate χ and a dark U(1)' gauge boson A' mediated by a dark Higgs S.
• Use a Mexican-hat potential for S to generate spontaneous U(1)' breaking with m_A'~MeV and m_φ~MeV scales.
• Compute the finite-temperature effective potential V_T(φ,T) including one-loop, thermal, and daisy contributions to model the FOPT.
• Solve for bubble nucleation via S3/T and determine nucleation temperature T_n and percolation dynamics.
• Apply the CosmoTransitions framework to obtain the GW spectrum from the FOPT, focusing on sound waves and turbulence contributions.
• Scan parameter space to identify benchmark points that fit both SIDM cross sections and PTA GW data.

Experimental results

Research questions

• RQ1 Can a MeV-scale first-order phase transition in the dark sector generate a dark mediator mass with properties suitable for SIDM?
• RQ2 Does the parameter space that yields SIDM self-interactions also reproduce the nano-Hertz GW signals reported by NANOGrav and CPTA?
• RQ3 What are the cosmological and astrophysical constraints on such a FOPT-driven SIDM model, and can viable benchmarks satisfy them?
• RQ4 What observable signatures (collider, direct detection, lepton-jet signals) can test the proposed U(1)' SIDM scenario?

Key findings

• Benchmark points exist where the DM self-interaction cross section matches requirements for dwarf galaxies and clusters (velocity-dependent σ̄/mχ in the ~1–10 cm^2/g range at 10–200 km/s, and ~0.2–0.5 cm^2/g at higher velocities).
• The FOPT temperature is MeV-scale, producing a stochastic GW signal with peak around ~10^(-8) Hz consistent with PTA observations.
• The model yields a MeV-scale mediator m_A' ~ 10 MeV naturally via spontaneous U(1)' breaking with realistic g' ~ O(1).
• PTA data (NANOGrav, CPTA) can be accommodated by the identified benchmark points alongside the SIDM requirements.
• The scenario remains consistent with BBN/CMB constraints for T_n ≳ 3 MeV when additional model features (e.g., operators linking dark and visible sectors) are considered.
• There are concrete collider and direct-detection avenues (e.g., lepton-jet signals, Higgs exotic decays, and kinetic mixing constraints) to test the framework.