In the standard model of cosmology anisotropies in the spacetime geometry quickly  dilute with the expansion, and are washed away during the very first instants of the inflationary era. In contrast, cosmic perturbations retain memory of primordial anisotropies for longer periods, since for them the effects dilute at a much slower rate, making it possible to leave an imprint in the cosmic microwave background (CMB). I will discuss these questions quantitatively, with special attention to loop quantum cosmology, and will argue that the expected traces of an anisotropic bounce would manifest themselves in the existence of quantum entanglement  between the primordial scalar and tensor perturbations, as well as direction dependent power spectra for large angular scales in the CMB.