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

TL;DR

This paper extends the scalar-induced gravitational wave framework to third order, showing it can better explain PTA signals and mitigate primordial black hole overproduction issues, supported by combined cosmological and PTA data.

Contribution

It introduces third-order gravitational waves into the SIGW model, enhancing spectral amplitude and addressing PBH overproduction while fitting observational data.

Findings

Third-order GWs can significantly boost SIGW spectral amplitude.

The model alleviates PBH overproduction constraints.

Results remain consistent when including SMBH binary background.

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.