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Since the very first observations, the Cosmic Microwave Background (CMB) hasrevealed on large-scales unexpected features known as anomalies, whichchallenge the standard $\Lambda$ cold dark matter ($\Lambda$CDM) cosmologicalmodel. One such anomaly is the "lack-of-correlation", where the measuredtwo-point angular correlation function of CMB temperature anisotropies iscompatible with zero, differently from the predictions of the standard model.This anomaly could indicate a deviation from the standard model, unknownsystematics, or simply a rare realization of the model itself. In this study,we explore the possibility that the lack-of-correlation anomaly is aconsequence of living in a rare realization of the standard model, byleveraging the potential information provided by the cosmological gravitationalwave background (CGWB) detectable by future gravitational wave (GW)interferometers. We analyze both constrained and unconstrained realizations ofthe CGWB to investigate the extent of information that GWs can offer. Toquantify the impact of the CGWB on the lack-of-correlation anomaly, we employestablished estimators and introduce a new estimator that addresses the"look-elsewhere" effect. Additionally, we consider three different maximummultipoles, denoted as $\ell_{\rm max}$, to account for the anticipatedcapabilities of future GW detectors ($\ell_{\rm max} = 4, 6, 10$). Summarizingour findings for the case of $\ell_{\rm max} = 4$, we identify the angularrange $[63^\circ - 180^\circ]$ as the region where future observations of theCGWB maximize the probability of rejecting the standard model. Furthermore, wecalculate the expected significance of this observation, demonstrating that98.81% (81.67%) of the GW realizations enhance the current significance of theanomaly when considering the full-sky (masked) Planck SMICA map as our CMB sky.

Unraveling the CMB lack-of-correlation anomaly with the cosmological gravitational wave background