[Paper Review] NANOGrav Signal from a Dark Conformal Phase Transition

Kohei Fujikura, Sudhakantha Girmohanta+2 more|arXiv (Cornell University)|Jun 29, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper proposes that the NANOGrav low-frequency gravitational wave signal originates from a first-order phase transition in a nearly-conformal dark sector thermally decoupled from the visible Standard Model. Using a 5D holographic model with a warped extra dimension, the authors show that the phase transition generates a stochastic gravitational wave background matching the NANOGrav data, while satisfying the ΔN_eff constraint in the secluded dark sector scenario and potentially alleviating the Hubble tension via dark radiation.

ABSTRACT

We explore the possibility that a confining first-order phase transition of a nearly-conformal dark sector generates the reported NANOGrav signal of a stochastic gravitational wave background. The visible Standard Model (SM) sector and the dark sector are initially thermally decoupled so that their temperatures are different. The nearly conformal phase transition is described by the shallow potential of a dilaton (or a radion in the 5D holographic perspective) generated by a new dark Yang-Mills field coupled to the conformal sector. For a dark sector only gravitationally connected with the visible sector, the NANOGrav signal is explained by the phase transition without contradicting the $ΔN_{ m eff}$ constraint, together with a contribution from supermassive black hole binaries. While the dilaton and dark glueballs can be produced after the phase transition, they immediately decay into dark radiation, which can help ameliorate the Hubble tension and be tested by the future CMB-S4 experiment. Alternatively, for a dark conformal sector decaying into the visible sector after the phase transition, the $ΔN_{ m eff}$ constraint is not applied and the phase transition can solely explain the NANOGrav signal.

Motivation & Objective

• To explain the NANOGrav stochastic gravitational wave background signal using a cosmological first-order phase transition in a nearly-conformal dark sector.
• To construct a concrete, weakly-coupled particle physics model—via a 5D holographic Randall-Sundrum setup—where the phase transition is driven by a new dark Yang-Mills field.
• To ensure consistency with cosmological constraints, particularly ΔN_eff, by considering both secluded and decaying dark sector scenarios.
• To explore the potential of the resulting dark radiation component to alleviate the Hubble tension and be probed by future CMB-S4 experiments.

Proposed method

• Model the nearly-conformal dark sector using a 5D holographic framework with a warped extra dimension, where the radion field mediates the phase transition.
• Construct a shallow potential for the radion (or dilaton) via a new 5D dark Yang-Mills field coupled to the conformal sector, enabling a strong first-order phase transition.
• Use the AdS/CFT correspondence to map the 5D holographic model to a 4D effective field theory, allowing computation of gravitational wave production from bubble collisions and sound waves.
• Compute the gravitational wave energy density parameter α′ using the formula α′ ≃ 0.07(ΔN_eff/0.5)(g*_s/g*_s0)^{4/3}(g*^{(D)}/g*^{(D)}_0)(g*_s0^{(D)}/g*_s^{(D)})^{4/3}, relating it to cosmological observables.
• Analyze two scenarios: (1) secluded dark sector, where dark radiation persists and affects ΔN_eff; (2) decaying dark sector, where ΔN_eff constraint is relaxed.
• Compare predicted GW spectra with the NANOGrav 15-year data, requiring α′ ≃ 0.1–10 and β/H_* ≃ 4–21 to match the observed signal amplitude.

(a)

Experimental results

Research questions

• RQ1 Can a confining first-order phase transition in a nearly-conformal dark sector produce a stochastic gravitational wave background consistent with the NANOGrav 15-year signal?
• RQ2 How does thermal decoupling between the dark and visible sectors affect the ΔN_eff constraint and the viability of the phase transition model?
• RQ3 What is the role of dark radiation produced after the phase transition in alleviating the Hubble tension?
• RQ4 Can a holographic 5D model with a warped extra dimension provide a weakly-coupled, calculable description of the phase transition dynamics?
• RQ5 How do different contributions—bubble collisions and sound waves—contribute to the gravitational wave amplitude, and what parameter ranges yield a fit to the NANOGrav data?

Key findings

• A confining first-order phase transition in a nearly-conformal dark sector can produce a stochastic gravitational wave background with amplitude α′ ≃ 0.1–10, matching the NANOGrav signal for β/H_* ≃ 4–21 and T_* ≃ 10 MeV–0.12 GeV.
• In the secluded dark sector scenario, the phase transition produces dark radiation that contributes to ΔN_eff ≃ 0.6, consistent with the conservative bound ΔN_eff < 0.7 and potentially ameliorating the Hubble tension.
• The model satisfies the ΔN_eff constraint only in the secluded dark sector case; in the decaying dark sector case, the constraint is relaxed, allowing larger α′ and stronger GW signals.
• The resulting dark radiation from decay of dilatons and glueballs after the phase transition can be probed by the future CMB-S4 experiment.
• The holographic 5D model with a warped extra dimension provides a viable, calculable framework for realizing a strong first-order phase transition via a radion potential generated by a new 5D dark Yang-Mills field.
• The model avoids the cosmological coincidence problem only partially, as the required energy density equality between dark and visible sectors at the phase transition remains a fine-tuning issue.

(b)