Induced Gravitational Wave interpretation of PTA data: a complete study for general equation of state

Understand

We thoroughly study the induced gravitational wave interpretation of the possible gravitational wave background reported by PTA collaborations, considering the unknown equation of state $w$ of the early universe.

• We perform a Bayesian analysis of the NANOGrav data using the publicly available \textsc{PTArcade} code together with \textsc{SIGWfast} for the numerical integration of the induced gravitational wave spectrum.
• We focus on two cases: a monochromatic and a log-normal primordial spectrum of fluctuations.
• For the log-normal spectrum, we show that, while the results are not very sensitive to $w$ when the GW peak is close to the PTA window, radiation domination is out of the $2\sigma$ contours when only the infra-red power-law tail contributes.