Towards a proof of the equivalence between FRW background expansion and statistical isotropy

We will expose in this paper our advances towards a proof of the equivalence between FRW background expansion, during some period of time that contains primordial inflation, and the statistical isotropy of the primordial curvature perturbation \(\zeta\) at the end of this period of time. Our motivation rests on the growing interest in the existence of a preferred direction in the Universe hinted by the continuous presence of anomalies in the CMB data.