SciPost logo

SciPost Submission Page

Search for scalar induced gravitational waves in the International Pulsar Timing Array Data Release 2 and NANOgrav 12.5 years datasets

by Virgile Dandoy, Valerie Domcke, Fabrizio Rompineve

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Fabrizio Rompineve
Submission information
Preprint Link: scipost_202302_00045v2  (pdf)
Date accepted: 2023-07-26
Date submitted: 2023-07-03 19:21
Submitted by: Rompineve, Fabrizio
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Phenomenology
Approaches: Theoretical, Computational, Phenomenological


We perform a Bayesian search in the latest Pulsar Timing Array (PTA) datasets for a stochastic gravitational wave (GW) background sourced by curvature perturbations at scales $10^5~\text{Mpc}^{-1}\lesssim k\lesssim 10^8~\text{Mpc}^{-1}$. These re-enter the Hubble horizon at temperatures around and below the QCD crossover phase transition in the early Universe. We include a stochastic background of astrophysical origin in our search and properly account for constraints on the curvature power spectrum from the overproduction of primordial black holes (PBHs). We find that the International PTA Data Release 2 significantly favors the astrophysical model for its reported common-spectrum process, over the curvature-induced background. On the other hand, the two interpretations fit the NANOgrav 12.5 years dataset equally well. We then set new upper limits on the amplitude of the curvature power spectrum at small scales. These are independent from, and competitive with, indirect astrophysical bounds from the abundance of PBH dark matter. Upcoming PTA data releases will provide the strongest probe of the curvature power spectrum around the QCD epoch.

Author comments upon resubmission

Dear Editor,

we thank you and the referee for the report.

We are resubmitting our manuscript following the referee report. We describe below the minor changes done to address the referee's point. We reply to referee in the comment section.

List of changes

1. We have added a clarification in our manuscript, at the end of the third paragraph on p. 10 (from "An alternative strategy" to "PTA data", mentioning the alternative strategy to set upper limits suggested by the referee and motivating our different strategy.

2. We have added a new reference in the caption of Fig. 6 (ref. 87 of the new version).

Published as SciPost Phys. Core 6, 060 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-7-4 (Invited Report)


This is a very timely paper to understand the observational possibilities of
induced gravitational wave.




The authors answered all of my questions. I recommend this paper to be published in this journal.

  • validity: good
  • significance: good
  • originality: ok
  • clarity: good
  • formatting: good
  • grammar: good

Login to report or comment