[Paper Review] Constraints On Scalar-Induced Gravitational Waves Up To Third Order From Joint Analysis of BBN, CMB, And PTA Data

Sai Wang, Zhichao Zhao+1 more|arXiv (Cornell University)|Jul 6, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy82 references8 citations

TL;DR

The paper jointly analyzes BBN, CMB, and PTA data to constrain scalar-induced gravitational waves up to third order, deriving tight bounds on the primordial curvature Spectrum and PBH mass range, and showing third-order SIGWs can dominate the energy density for certain amplitudes.

ABSTRACT

Recently, strong evidence for a gravitational wave background has been reported by collaborations of pulsar timing arrays (PTA). In the framework of scalar-induced gravitational waves (SIGWs), we concurrently investigate the second and third order gravitational waves by jointly analyzing PTA data, alongside big-bang nucleosynthesis (BBN), and cosmic microwave background (CMB) datasets. We determine the primordial curvature spectral amplitude as $0.021

Motivation & Objective

• Motivate constraints on scalar-induced gravitational waves (SIGWs) from early-universe probes (BBN, CMB) and PTA data.
• Extend SIGW calculations to include up to third order perturbations and assess their impact.
• Derive joint constraints on the primordial curvature spectrum amplitude A_zeta and peak frequency f_star.
• Infer implications for primordial black hole (PBH) mass ranges from SIGW interpretations of PTA data.

Proposed method

• Derive the third-order SIGW power spectrum using the sourced perturbations from first- and second-order scalar modes.
• Adopt a delta-function primordial curvature spectrum P_zeta(k)=A_zeta k_star delta(k-k_star) for simplicity.
• Compute the present-day energy-density fraction Omega_GW,0 and its dependence on A_zeta and f_star (including second and third order contributions).
• Perform Bayesian analysis of NG15 PTA data with priors on log10(f_star) and log10(A_zeta).
• Incorporate BBN and CMB indirect bounds via the integrated energy-density constraint to refine the joint posterior.

Experimental results

Research questions

• RQ1 What are the allowed ranges for the amplitude A_zeta and peak frequency f_star of the primordial curvature perturbations when SIGWs are considered up to third order?
• RQ2 How do second- and third-order SIGWs compare in their contribution to the integrated energy density, and under what conditions does the third order dominate?
• RQ3 What PBH mass range is implied if the PTA signal is due to SIGWs, given the joint BBN-CMB-PTA constraints?
• RQ4 How do BBN and CMB bounds alter the PTA-derived constraints in scenarios with only second order vs both second and third order SIGWs?
• RQ5 What are the prospects for future GW probes (e.g., SKA, space-borne detectors) to test these SIGW scenarios?

Key findings

• Joint analysis yields 95% C.L. constraints: 0.021 < A_zeta < 0.085 and 5.0e-8 Hz < f_star < 5.0e-7 Hz.
• Including third-order SIGWs strengthens the upper bound on A_zeta compared to second order alone in Scenario II.
• For A_zeta ≳ 0.06, third-order SIGWs contribute more to the integrated energy density than second-order SIGWs.
• The implied PBH mass range is 1e-4.5 M_sun < m_PBH < 1e-2.5 M_sun under the SIGW interpretation of the PTA signal.
• CMB constraints are competitive with or comparable to scenarios where all dark matter is PBH (PBH fraction f_PBH = 1).
• Future PTA, SKA, and space-based detectors could further test the inferred parameter region and improve measurements of the primordial curvature spectrum.