Cosmological consequences of statistical inhomogeneity

A space-dependent mean for cosmological perturbations negates the ansatz of statistical homogeneity and isotropy, and hence ergodicity. In this work, we construct such a primordial mean of scalar perturbations from an alternative quantum initial state (coherent state) and examine the associated power and bi-spectra. A multitude of cosmological tests based on these spectra are discussed. We find that current cosmological data doesn't favor a primordial mean over large scales and strong constraints arise from the limit on bispectrum from Planck data. At small scales, this hypothesis can be tested by future observables such as $\mu$-distortion of CMB.