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The presence of CMB Hemispherical Asymmetry (HPA) challenges the currentunderstanding of inflationary cosmology which does not generically predict theparity violation in the primordial correlations. In this paper, we shall reviewthe recently proposed resolution to this based on a new formulation ofquantizing inflationary fluctuations by focusing on the discrete spacetimetransformations in a gravitational context. The predictive power of thisformulation is that one can generate a scale dependent HPA in the context ofsingle field inflation for all the primordial modes including scalar and tensorfluctuations without introducing any additional parameters. This result can beseen as an indication of spontaneous breaking of$\mathcal{C}\mathcal{P}\mathcal{T}$ symmetry in an expanding Universe, ifconfirmed by future observations it would be a great leap in the subject ofquantum field theory in curved spacetime.

A robust explanation of CMB anomalies with a new formulation of inflationary quantum fluctuations