[Paper Review] Nano-Hertz gravitational waves from collapsing domain walls associated with freeze-in dark matter in light of pulsar timing array observations

Zhao Zhang, Chengfeng Cai+4 more|arXiv (Cornell University)|Jul 21, 2023

Superconducting and THz Device TechnologyPhysics and Astronomy126 references3 citations

TL;DR

This paper proposes a unified model where nano-hertz gravitational waves from collapsing domain walls—triggered by a radiatively induced $Z_2$-violating potential—explain pulsar timing array (PTA) observations, while the same feebly coupled fermion field produces dark matter via the freeze-in mechanism. The model simultaneously fits the NANOGrav GW signal and the observed dark matter relic density for $y_\chi \sim 10^{-10}$, $m_\chi \sim 0.17-7.5$ GeV, and $m_s \sim 8.1\times10^4 - 10^6$ GeV.

ABSTRACT

Evidence for a stochastic gravitational wave background in the nHz frequency band is recently reported by four pulsar timing array collaborations NANOGrav, EPTA, CPTA, and PPTA. It can be interpreted by gravitational waves from collapsing domain walls in the early universe. We assume such domain walls arising from the spontaneous breaking of a $Z_2$ symmetry in a scalar field theory, where a tiny $Z_2$-violating potential is required to make domain walls unstable. We propose that this $Z_2$-violating potential is radiatively induced by a feeble Yukawa coupling between the scalar field and a fermion field, which is also responsible for dark matter production via the freeze-in mechanism. Combining the pulsar timing array data and the observed dark matter relic density, we find that the model parameters can be narrowed down to small ranges.

Motivation & Objective

• To reconcile the recent PTA observations of a stochastic gravitational wave background (SGWB) in the nHz band with a cosmological origin in collapsing domain walls.
• To explain the observed dark matter relic density via the freeze-in mechanism using a feebly interacting fermion.
• To construct a dynamical link between the $Z_2$-violating potential needed for domain wall collapse and the same Yukawa coupling responsible for dark matter production.
• To constrain model parameters using both PTA GW data and the measured dark matter abundance, ensuring cosmological consistency.

Proposed method

• Introduce a real scalar field $S$ with a spontaneously broken $Z_2$ symmetry, leading to domain wall formation in the early universe.
• Include a tiny $Z_2$-violating potential induced at one-loop level via a Yukawa coupling $y_\chi$ between $S$ and a fermion $\chi$, which destabilizes the domain walls.
• Model the fermion $\chi$ as a feebly interacting massive particle (FIMP) produced via the freeze-in mechanism, with its relic density calculated from the one-loop-induced $\kappa_1$ term.
• Compute the gravitational wave spectrum from collapsing domain walls using the energy density and dynamics of the wall collapse, derived from the induced $Z_2$-violating potential.
• Use Bayesian posterior distributions from NANOGrav and EPTA data to constrain the GW amplitude and frequency, and compare with the predicted $\Omega_{\rm GW}^{\rm peak}$.
• Simultaneously impose constraints from Big Bang Nucleosynthesis (BBN) and domain wall overclosure to restrict viable parameter space.

Experimental results

Research questions

• RQ1 Can the observed nHz stochastic gravitational wave background in pulsar timing arrays be explained by collapsing domain walls arising from a $Z_2$-symmetric scalar field theory with a radiatively induced $Z_2$-violating potential?
• RQ2 Is it possible to simultaneously account for the observed dark matter relic density and the PTA GW signal using the same underlying physics, specifically a single Yukawa coupling?
• RQ3 What are the allowed ranges of the Yukawa coupling $y_\chi$, fermion mass $m_\chi$, and scalar mass $m_s$ that satisfy both the PTA GW data and the measured dark matter abundance?
• RQ4 How do cosmological constraints—particularly domain wall overclosure and BBN—limit the viable parameter space in this model?
• RQ5 Can the tiny $Z_2$-violating potential required for domain wall collapse be naturally generated at one-loop level via a feeble Yukawa coupling?

Key findings

• The model successfully explains the NANOGrav and EPTA observations of a stochastic gravitational wave background in the nHz band through collapsing domain walls.
• The required $Z_2$-violating potential is naturally generated at one-loop level via a Yukawa coupling $y_\chi \sim 10^{-10}$, consistent with the freeze-in mechanism for dark matter.
• The fermion $\chi$ with mass $m_\chi \sim 0.17-7.5$ GeV and coupling $y_\chi \in (4.6\times10^{-10}, 8.7\times10^{-10})$ can reproduce the observed dark matter relic density $\Omega_\chi h^2 = 0.12$.
• The scalar mass is constrained to $m_s \in (8.1\times10^4, 10^6)$ GeV for $\lambda_S = 0.2$, ensuring the domain walls collapse before overclosing the universe.
• The parameter region favored by the NANOGrav 95% credible interval overlaps with the dark matter relic density constraint, and the intersection occurs only for $y_\chi \in (4.6\times10^{-10}, 8.7\times10^{-10})$, indicating a tight but viable window.
• Cosmological constraints from BBN and domain wall overclosure do not exclude the NANOGrav 95% credible region, confirming the model's viability.