Translating nano-Hertz gravitational wave background into primordial perturbations taking account of the cosmological QCD phase transition

TL;DR

This paper investigates how the QCD phase transition affects the interpretation of nano-Hertz gravitational wave background data, providing refined constraints on primordial curvature perturbations.

Contribution

It introduces a method to incorporate the QCD phase transition into models of induced GWs and revises constraints on primordial perturbations accordingly.

Findings

QCD phase transition modifies the GW spectrum in the nano-Hertz range.

Neglecting QCD effects can underestimate the amplitude by about 25%.

Spectral index estimates can be off by up to 10%.

Abstract

The evidence of the nano-Hertz stochastic gravitational wave (GW) background is reported by multiple pulsar timing array collaborations. While a prominent candidate of the origin is astrophysical from supermassive black hole binaries, alternative models involving GWs induced by primordial curvature perturbations can explain the inferred GW spectrum. Serendipitously, the nano-Hertz range coincides with the Hubble scale during the cosmological quantum chromodynamics (QCD) phase transition. The influence of the QCD phase transition can modify the spectrum of induced GWs within the nano-Hertz frequency range, necessitating careful analysis. We estimate GWs induced by power-law power spectra of primordial curvature perturbations taking account of the QCD phase transition. Then we translate the implication of the NANOGrav data into the constraint on the power spectrum of the primordial curvature perturbation, which suggests one would underestimate the amplitude by about $25\%$ and the spectral index by up to $10\%$ if neglecting the QCD effect.