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

Author(s)

Iania, William, Ricciardone, Angelo

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.

Figures

Caption

Squared kernel before and after the oscillation average in~\cref{eq:temp_I_eMD} as a function of $x=k\eta$.

Caption

Energy density in~\cref{eq:general_Omega_reg}, normalized by the primordial amplitudes, from an eMD epoch and sudden transition to RD at $\eta_\R=2\times 10^{-6}\,\rm{Mpc}$, as a function of $k$. The log-normal primordial power spectra have same peak $k_\ast=6.47\times 10^{6}\,\rm{Mpc}^{-1}$ (corresponding to a physical frequency $f_\ast \simeq 10^{-8}\,\rm{Hz}$), and various values of $\sigma$, including $\sigma\to0$, i.e., the monochromatic limit.

Caption

Corner plots for STGWs+PGWs generated during an early matter domination that suddenly interrupts transiting to the standard RD epoch. We used lognormal primordial power spectra with same peak and width, and NG15 data, fixing $\eta_{R}=2\times10^{-6}\,\rm{Mpc}^{-1}$. The plots show the 68\% and 95\% credible regions, whereas the red areas are the subspaces cutted out by the PBH overproduction.

Caption

Left panel: Bayesian MCMC parameter estimation obtained from SKA-like configuration with $T_\text{obs}=10.33$ yr and $N_\text{p}=200$, using STGWs from an eMD epoch, fixing $\eta_\R=2\times10^{-6}\,\rm{Mpc}^{-1}$. Right panel: the same Bayesian estimation, adding the contribution of the linear-order PGWs. The shaded regions show the constraints from PBH overproduction. Log-normal primordial power spectra with same shape parameters are used as scalar and tensor seeds.

Caption

Left panel: Bayesian MCMC parameter estimation obtained from SKA-like configuration with $T_\text{obs}=10.33$ yr and $N_\text{p}=200$, using STGWs generated during the RD epoch. Right panel: same Bayesian estimation adding the contribution of the PGWs. The shaded regions are forbidden by PBH overproduction. Scalar and tensor seeds are both log-normal power spectra with same peak frequency and width.

Caption

STGWs generated during early matter domination by log-normal and monochromatic input power spectra, as a function of $f$, for some values of peak frequency and width.

Caption

STGWs generated during early matter domination by log-normal and monochromatic input power spectra, as a function of $f$, for some values of peak frequency and width.

Caption

STGWs generated during early matter domination by log-normal and monochromatic input power spectra, as a function of $f$, for some values of peak frequency and width.

Caption

STGWs generated during early matter domination by log-normal and monochromatic input power spectra, as a function of $f$, for some values of peak frequency and width.

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