AR_final file_2018-19

Quantum Theory and Gravity Quantum correlators in Friedmann space- times: The omnipresent de Sitter and the invariant vacuum noise The study of quantum fields in Friedmann uni- verses is relevant to identify the seeds of structure formation as the quantum fluctuations in the early universe. Numerous investigations in this direction have highlighted several theoretical issues, which are rather special to this context, especially for the de Sitter (dS) universe. To shed more light on some of these issues, we revisit the study of a massive scalar field minimally coupled to a Friedman uni- verse with the scale factor proportional to some power of the conformal time coordinate. • Equivalence between dynamics of a quantum field in one Friedmann uni- verse and that of another field in another Friedmann universe : T. Pad- manabhan and Karthik Rajeev have shown that the dynamics of a massive scalar field (say φ, m ) on a cosmological Friedmann background (with scale factor, say, a ) can be mapped to that of another scalar field ( ψ, m ′ ) in another Friedmann universe (with scale factor b ). A special case of this equivalence is of particular interest; a massless scalar field in any power law cosmology (i.e., when a ( η ) ∝ η − q ) can be mapped to a massive field in a dS spacetime, where the mass, M , of the field in the dS spacetime is determined by M 2 = (2 + q )(1 − q ). A massive field in dS is well-studied and fairly well-understood system, hence, through this mapping, one can gain insights about the features of a massless field in the background of a less symmetric spacetime, namely the power-law Friedmann universe. In particular, massless scalar fields in different phases of the Universe (e.g., radiation era, matter era, etc.) can be studied using this approach. • Massless field in dS: The two-point corre- lation function for massive scalar field in dS background is a well studied subject. The massless limit of this correlation function is known to be pathological. This feature is usu- ally attributed to breakdown of a symmetry in the case of a massless scalar field in dS. Pad- manabhan and Karthik have shown that the divergences (pathologies) for massless scalar fields occur in any power law cosmology with a negative equation of state parameter ( w ). Note that, such power-law cosmologies, with − 1 < w < 0, have no special symmetries un- like the dS background, which corresponds to w = − 1. Hence, they find that the divergent two-point function is intimately coupled with the character of the source supporting the ge- ometry. In particular, the pathology in dS is also due to the negative value of the equation of state parameter, namely w = − 1, and has no special relationship to dS invariance or its breakdown. • Power spectrum through Killing direc- tions: Power spectrum is one of the important characterizations of the quantum fluctuations of a field. Padmanabhan and Karthik have developed a machinery to obtain the power spectrum in a Friedmann universe through its Killing vectors. This new approach provides a geometric picture of the power spectrum for different cosmologies, including the dS uni- verse. • Persistent vacuum noise: Padmanabhan and Karthik have demonstrated that a quan- tum scalar field in a Friedmann universe hosts a curvature-dependent minimum vacuum noise (vacuum power spectrum). This persistent noise corresponds to the large wavelength limit in the power spectrum. For example, the dS spacetime always has a ∼ H 2 vacuum noise, a feature that is reflected in the well known scale invariant power spectrum. By adopting trajectories for which the chosen state does not remain the ‘natural vacuum’, one can en- hance this noise. In particular, using the co-moving/static observer correspondence in the dS spacetime, they show how the persis- tent vacuum noise gets enhanced by stimulated emission . An analogous result holds in the ( 55 )