Probing Scalar-Tensor-Induced Gravitational Waves in the nHz Band: $\texttt{NANOGrav}$ and SKA

TL;DR

This paper analyzes scalar-tensor-induced gravitational waves in the nanohertz band, assessing their potential to explain PTA signals and be detected by SKA, considering different cosmological eras and their contributions.

Contribution

It computes the spectrum of scalar-tensor-induced GWs during matter-dominated eras and forecasts their detectability with future PTA and SKA observations.

Findings

STGWs can remain significant during an early matter-dominated epoch.

Scalar-tensor-induced GWs could dominate the stochastic background in certain scenarios.

Future observations like SKA may detect these scalar-tensor-induced gravitational waves.

Abstract

Scalar-induced gravitational waves (SIGWs) have recently attracted considerable interest, both as a possible explanation for the nanohertz signal reported by the Pulsar Timing Array (PTA) collaboration and for their connection with primordial black hole (PBH) physics. In addition to SIGWs, scalar-tensor-induced gravitational waves (STGWs) have emerged as a promising cosmological source of the stochastic gravitational wave background (SGWB). In this paper, we compute the STGWs generated during a generic matter-dominated (MD) era, as well as during an early matter-dominated (eMD) epoch followed by a sudden transition to the standard radiation-dominated (RD) stage, working in the Poisson gauge. We find that, in a purely MD age, the corresponding energy density rapidly dilutes, whereas in the presence of an eMD phase it remains non-vanishing due to the short duration of the eMD period. We then investigate whether the STGW signal could provide a dominant contribution to the $\texttt{NANOGrav 15-year}$ dataset and we forecast the prospects for its detection with future observations by the Square Kilometre Array (SKA). In particular, we consider STGWs generated during both eMD and RD eras, including their linear-order contributions. Our results show that the GWs induced by scalar-tensor mixing constitute a viable target for future, more sensitive detections of the SGWB.