From Quantum to Classical in the Sky

Abstract

Inflation has by-far set itself as one of the prime ideas in the current cosmological models that seemingly has an answer for every observed phenomenon in cosmology. More importantly, it serves as a bridge between the early quantum fluctuations and the present-day classical structures. Although the transition from quantum to classical is still not completely understood till date, there are two assumptions made in the inflationary paradigm in this regard: (i) the modes (metric perturbations or fluctuations) behave classically once they are well outside the Hubble radius and, (ii) once they become classical they stay classical and hence can be described by standard perturbation theory after they re-enter the Hubble radius. We critically examine these assumptions for the tensor modes of (linear) metric perturbations in a toy three stage universe with (i) inflation, (ii) radiation-dominated and (iii) late-time accelerated phases. The quantum-to-classical transition for these modes is evident from the evolution of Wigner function in phase space and its peaking on the classical trajectory. However, a better approach to quantify the degree of classicality and study its evolution was given by Mahajan and Padmanabhan [1] using a classicality parameter constructed from the parameters of the Wigner function. We study the evolution of the classicality parameter across the three phases and it turns out that the first assumption holds true, there is emergence of classicality on Hubble exit, however the latter assumption of "once classical, always classical" seems to lie on a shaky ground.