[Paper Review] Constraining Cosmological Phase Transitions with Chinese Pulsar Timing Array Data Release 1

Deng Wang|arXiv (Cornell University)|Jul 29, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper uses Chinese Pulsar Timing Array Data Release 1 (CPTA-DR1) to constrain first-order cosmological phase transitions, finding its sensitivity to gravitational wave backgrounds from such transitions is slightly stronger than NANOGrav’s 12.5-year data but weaker than its 15-year data. The analysis sets a 2σ constraint on phase transition temperature at log₁₀T⋆ = −1.12⁺².⁵⁹₋₁.⁷⁵, ruling out transitions below 1.3 MeV and allowing a range of [1.3 MeV, 29.5 GeV].

ABSTRACT

The Chinese Pulsar Timing Array (CPTA) collaboration has recently reported the observational evidence of a stochastic gravitational wave background. In light of the latest CPTA observation, we aim at exploring the ability of CPTA in probing new physics. Specifically, we constrain the first-order cosmological phase transitions with CPTA data, and find that the constraining result is slightly tighter than that of NANOGrav's 12.5-yr data but weaker than NANOGrav's 15-yr data. Considering the possible complexity of gravitational wave sources, we give the constraint on a mixed scenario of cosmological phase transitions and astrophysical supermassive binary black holes. Our analysis suggests that CPTA has a great potential to probe fundamental physics in the near future.

Motivation & Objective

• To assess the constraining power of CPTA-DR1 data on first-order cosmological phase transitions via gravitational wave (GW) background detection.
• To compare CPTA-DR1's sensitivity with existing NANOGrav datasets (12.5-yr and 15-yr) in probing phase transition parameters.
• To investigate the impact of mixed astrophysical (supermassive binary black holes) and cosmological GW sources on parameter degeneracy and constraints.
• To evaluate the effectiveness of external constraints from CMB, BBN, and astrometry in tightening phase transition parameter space.
• To determine the potential of CPTA to probe new physics in the early universe using low-frequency GW signals.

Proposed method

• Utilizes CPTA-DR1 data from 57 millisecond pulsars observed with FAST between April 2019 and September 2022, covering a frequency of ~14 nHz.
• Applies Bayesian inference to model the stochastic gravitational wave background (SGWB) using a 4-parameter model for first-order phase transitions: phase transition temperature T⋆, strength α⋆, bubble wall velocity vw, and inverse duration H⋆/β.
• Employs the Hellings-Downs correlation pattern to identify SGWB from cosmological sources, distinguishing it from astrophysical noise.
• Compares results with NANOGrav’s 12.5-yr and 15-yr analyses to benchmark CPTA-DR1’s sensitivity and constraining power.
• Extends the analysis to a mixed PTBBH model that includes both cosmological phase transitions and supermassive binary black hole (SMBBH) mergers, introducing nine free parameters.
• Incorporates external constraints from CMB, Big Bang Nucleosynthesis (BBN), and astrometry (ΩGW < 10⁻⁶) to test their impact on parameter space compression.

Experimental results

Research questions

• RQ1 How does the constraining power of CPTA-DR1 on cosmological phase transitions compare to that of NANOGrav’s 12.5-year and 15-year datasets?
• RQ2 What are the 2σ constraints on the phase transition temperature T⋆, strength α⋆, and duration H⋆/β from CPTA-DR1?
• RQ3 How do parameter degeneracies between phase transition parameters and SMBBH parameters affect the sensitivity of CPTA-DR1?
• RQ4 To what extent do external constraints from CMB, BBN, and astrometry improve the bounds on cosmological phase transition parameters?
• RQ5 What is the inferred merger rate density of supermassive binary black holes in a mixed cosmological-astrophysical GW scenario?

Key findings

• CPTA-DR1 constrains the phase transition temperature to log₁₀T⋆ = −1.12⁺².⁵⁹₋₁.⁷⁵ at 2σ confidence level, excluding transitions below 1.3 MeV.
• The allowed phase transition temperature range is [1.3 MeV, 29.5 GeV] at 2σ, which is slightly tighter than NANOGrav’s 12.5-yr result but less constraining than its 15-yr result.
• CPTA-DR1 sets a lower bound of H⋆/β > 0.014 and a lower bound of α⋆ > 0.21 at 2σ, with an upper bound on friction η < 8.12.
• The inclusion of integrated constraints from CMB, BBN, and astrometry (ΩGW < 10⁻⁶) provides negligible improvement in constraining the phase transition parameter space.
• In the mixed PTBBH model, the BBH merger rate density is constrained to log₁₀(ṅ₀/Mpc⁻³Gpc⁻¹) = −5.28⁺⁴.⁴¹₋⁸.⁹⁹ at 1σ, indicating weak constraints on astrophysical parameters.
• Parameter degeneracies remain strong, especially between α⋆ and η, and the inclusion of SMBBH sources significantly enlarges the allowed phase transition parameter space compared to the pure PTO model.