Reassessing the SIGW Interpretation of PTA Signal: The Role of Third-Order Gravitational Waves and Implications for the PBH Overproduction

Abstract

In light of recent interpretations attributing pulsar timing array (PTA) signal to second-order gravitational waves induced by linear cosmological curvature perturbations in the early universe, the overproduction of primordial black holes (PBHs) poses a theoretical tension. In this work, we address this issue through extending such a scalar-induced gravitational wave (SIGW) framework to include third-order gravitational waves, which allow for a substantial enhancement in the spectral amplitude of SIGWs. Analyzing a combined dataset from cosmic microwave background and baryon acoustic oscillations, we derive cosmological constraints on the physical energy-density fraction of cosmological gravitational waves. Further incorporating PTA data, we obtain constraints on the spectral amplitude and peak frequency of SIGWs. Our results indicate that the parameter region favored by the data combination can to some extent alleviate the PBH overproduction problem, thereby supporting the theoretical consistency of our model. Furthermore, we demonstrate the robustness of our SIGW interpretation for the PTA signal by extending the analysis to include a gravitational wave background from supermassive black hole binaries. These findings are poised for further scrutiny with future high-precision observations.

Figures (5)

• Figure 1: Illustrative figure for the SIGW energy-density fraction spectra. The blue solid curve shows the contribution from second-order components only, while the red solid curve includes both second- and third-order components. Both spectra are computed using the same parameter set $(A_\zeta, f_\ast)$, corresponding to the median values in the joint PTA, CMB, and BAO constraints on the SIGW spectrum (i.e., the first row of Tab. \ref{['tab:inferenceres']}). The grey violins represent the NG15 dataset NANOGrav:2023hvm.
• Figure 2: One-dimensional posterior distributions of $\omega_{t}$ obtained via analyzing the CMB-SPA and DESI DR2 observational data (blue) and the LiteBIRD, S4, and CSST mock data (orange).
• Figure 3: One- and two-dimensional posterior distributions of the independent parameters inferred from the joint data analysis. Dark and light shaded regions, respectively, stand for 68% and 95% CL. Dashed vertical lines represent 68% CL boundaries.
• Figure 4: The same as Fig. \ref{['fig:posteriorsfin3']}, but we use the mock data of the next-generation CMB and BAO experiments.
• Figure 5: Two-dimensional posterior distributions of $A_{\zeta}$ and $f_{\ast}$ versus the $f_{\mathrm{PBH}}=1$ contour. We depict the left/right panel using the posteriors derived in Fig. \ref{['fig:posteriorsfin3']}/ Fig. \ref{['fig:posteriorsfin']}. For comparison, we depict the $f_{\mathrm{PBH}}=1$ contour in black dashed curves.