[Paper Review] Domain Wall Network: A Dual Solution for Gravitational Waves and Hubble Tension?

Ligong Bian, Shuailiang Ge+3 more|arXiv (Cornell University)|Dec 15, 2022

Pulsars and Gravitational Waves Research6 references5 citations

TL;DR

This paper proposes that a domain wall network in the early Universe could simultaneously explain the nano-hertz stochastic gravitational wave background detected by the Parkes Pulsar Timing Array and the Hubble tension. It shows that a wall tension of $\sigma_{\rm DW} \sim (29-414\ \text{TeV})^3$ and decay temperature $T_d \sim 20-257\ \text{MeV}$ can account for the observed common power-law process while also generating free particles that decay into dark radiation, reducing the Hubble tension from 4.1σ to 2.7σ.

ABSTRACT

We explore the possibility that domain wall networks generate the stochastic gravitational wave background (SGWB) observed as a strong common power-law process in the Data Release-2 of Parkes Pulsar Timing Array. We find that a broad range of parameters, specifically wall tension around $σ_{ extrm{DW}} \sim (29-414 , extrm{TeV})^3$ and wall-decay temperature within $T_d \sim 20-257 , extrm{MeV}$, can explain this phenomenon at a $68\%$ credible level. Meanwhile, the same parameters could ease the Hubble tension if particles from these domain wall networks decay into dark radiation. We establish a direct analytical relationship, $Ω_{ extrm{GW}}(f_p,T_0) h^2 \sim Ω_{ extrm{rad}} h^2 ( Ω_νΔN_{ extrm{eff}})^2$, to illustrate this coincidence, underlining its importance in the underlying physics and potential applicability to a wider range of models and data. Conversely, if the common power-law process is not attributed to domain wall networks, our findings impose tight limits on the wall tension and decay temperature.

Motivation & Objective

• To investigate whether domain wall networks can explain the common power-law process observed in the Parkes Pulsar Timing Array's Data Release-2.
• To assess whether the same domain wall parameters can alleviate the Hubble tension by producing dark radiation from decayed free particles.
• To establish robust constraints on domain wall parameters if the common power-law process is not of domain wall origin.
• To explore the consistency of this dual solution across multiple Pulsar Timing Array collaborations.
• To map the domain wall parameters to axion models and assess compatibility with existing and future axion searches.

Proposed method

• The authors analyze the Parkes Pulsar Timing Array's second data release to search for a stochastic gravitational wave background (SGWB) from domain wall networks.
• They model the SGWB spectrum as a broken power-law, characteristic of domain wall dynamics, and compare it to the observed common power-law process.
• The domain wall network's energy density evolves as $\rho_{\rm DW} \propto H(t)$, with energy released via gravitational waves and free particles.
• The free particles are assumed to decay into dark radiation, which modifies the effective number of relativistic degrees of freedom, thereby reducing the Hubble tension.
• The likelihood analysis is performed at 68% credible level to determine allowed parameter regions for wall tension and decay temperature.
• The study also considers alternative hypotheses—such as the signal arising from supermassive black hole binaries or an unknown background—to derive conservative constraints on domain wall parameters.

Experimental results

Research questions

• RQ1 Can a domain wall network explain the common power-law process observed in the Parkes Pulsar Timing Array's Data Release-2?
• RQ2 Does the same domain wall parameter space that explains the gravitational wave signal also alleviate the Hubble tension?
• RQ3 How robust is the coincidence between explaining the SGWB and reducing the Hubble tension across different Pulsar Timing Array datasets?
• RQ4 What are the constraints on domain wall parameters if the common power-law process is not due to domain walls?
• RQ5 Can the domain wall model be embedded in the QCD axion framework, and are the predicted axion masses consistent with current and future experimental searches?

Key findings

• A domain wall network with wall tension $\sigma_{\rm DW} \sim (29-414\ \text{TeV})^3$ and decay temperature $T_d \sim 20-257\ \text{MeV}$ can explain the common power-law process in the Parkes Pulsar Timing Array's Data Release-2 at 68% credible level.
• The same parameter region reduces the Hubble tension from 4.1σ to 2.7σ when the free particles from domain wall decay produce dark radiation.
• This dual explanation is robust and independent of specific domain wall properties, holding across different Pulsar Timing Array collaborations including NANOGrav, EPTA, and CPTA.
• If the common power-law process is not due to domain walls, the study sets stringent constraints on domain wall parameters, ruling out a broad range of $\sigma_{\rm DW}$ and $T_d$ at 95% confidence level.
• The preferred domain wall parameters map to axion masses in the range $m_a \sim 10^{-13}-10^{-8}\ \text{eV}$, consistent with current and future axion search experiments.
• The results remain consistent across different network sizes ($N_{\rm DW}$), indicating the robustness of the parameter space.