Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background

TL;DR

The paper investigates how cross-correlations between scalar-induced gravitational wave (SIGW) energy-density anisotropies and cosmic microwave background (CMB) temperature and E-mode polarization can constrain local-type primordial non-Gaussianity parameters $f_{\rm NL}$ and $g_{\rm NL}$. It derives the cross-angular power spectra $C_{\ell}^{\rm XG}$ and the SIGW auto-spectrum $C_{\ell}^{GG}$, incorporating non-adiabatic initial conditions and the Sachs–Wolfe-like SW/ISW effects, and uses a Fisher-matrix framework to forecast sensitivities for future GW detectors and CMB experiments. The results show that the cross-spectra are highly sensitive to $f_{\rm NL}$ and can alleviate parameter degeneracies when combined with auto-correlations, enabling improved measurements of non-Gaussianity; DECIGO, among other detectors, can approach cosmic-variance limits under favorable conditions. Overall, the work proposes a novel avenue to probe the early universe by leveraging multi-band SIGW–CMB cross-correlations, with potential to distinguish SIGW signals from astrophysical foregrounds and to illuminate inflationary dynamics.

Abstract

The stochastic gravitational-wave background originating from cosmic sources contains vital information about the early universe. In this work, we comprehensively study the cross-correlations between the energy-density anisotropies in scalar-induced gravitational waves (SIGWs) and the temperature anisotropies and polarization in the cosmic microwave background (CMB). In our analysis of the angular power spectra for these cross-correlations, we consider all contributions of the local-type primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ that can lead to large anisotropies. We show that the angular power spectra are highly sensitive to primordial non-Gaussianity. Furthermore, we project the sensitivity of future gravitational-wave detectors to detect such signals and, consequently, measure the primordial non-Gaussianity.

Figures (5)

• Figure 1: The angular power spectra for the auto- and cross-correlations are shown with CV shaded. For illustration, we depict them in the frequency band of $\nu=f_{p}$ by assuming the model parameters $A_{S}=0.02$, $\sigma=1$, $f_{\mathrm{NL}}=\pm10$ (plus in solid while minus in dashed), and $g_{\mathrm{NL}}=20$. The shaded region shows the $\pm1\sigma$ (68% C.L.) uncertainty from CV only.
• Figure 2: We show dependence of the angular power spectra on frequency bands. For the purpose of illustration, we fix $\ell=4$ and the model parameters $A_{S}=0.02$, $\sigma=1$, $f_{\mathrm{NL}}=10$, and $g_{\mathrm{NL}}=20$.
• Figure 3: Comparison between the signal and the optimal sensitivity of detectors. The noise level of NANOGrav is illustrated as the lowest in the lower panel of Fig. 4 in Ref. Pol:2022sjn, while the noise levels of other detectors are depicted in Fig. 7 of Ref. Braglia:2021fxn. In our analysis, we consider a set of model parameters $f_{\mathrm{NL}}=10$, $g_{\mathrm{NL}}=0$, $A_{S}=0.02$, $\sigma=1$, and $f_{p}=f_{\ast}$ with $f_{\ast}$ being the frequency associated with the optimal sensitivity. For the signal, we utilize the specified auto-correlated angular power spectrum at $\nu=f_{p}$.
• Figure 4: The SNR are depicted for the detection of auto-correlations (dashed curves) and both auto- and cross-correlations (solid curves) using future gravitational-wave detectors. We adopt the same set of model parameters as those in Fig. \ref{['fig:Fig5']}. For comparison, we include the CV limits. It is worth noting that the curves corresponding to DECIGO perfectly align with the CV limits.
• Figure 5: The uncertainties in $f_{\mathrm{NL}}$ are assessed by measuring the auto-correlations (dashed curves) and both auto- and cross-correlations (solid curves) using prospective gravitational-wave detectors. We use $\ell_{\mathrm{max}}=6$ for NANOGrav while $\ell_{\mathrm{max}}=30$ for others. For each $f_{\mathrm{NL}}$ value, we calculate $A_{S}$ setting $\mathrm{SNR}=1$ in the auto-correlation-only case, while assuming $g_{\mathrm{NL}}=0$, $\sigma=1$, and $f_{p}=f_{\ast}$.