Dipayan Mukherjee, H. V. Ragavendra, Shiv K. Sethi

We investigate the impact of statistical inhomogeneity and anisotropy in primordial scalar perturbations on the scalar-induced gravitational waves (SIGW). Assuming inflationary quantum fluctuations originate from a coherent state, the resulting primordial scalar perturbations acquire a non-zero space-dependent mean, violating statistical homogeneity, statistical isotropy, and parity. As a consequence of statistical inhomogeneities, SIGW acquires distinct scale-dependent features in its correlation function. Statistical anisotropies further lead to possible parity violation and correlation between different polarization modes in the tensor perturbations. Therefore, detection of these signatures in the stochastic gravitational wave background would offer probes to the statistical nature of primordial scalar perturbations beyond the scales accessible to CMB observations.