Cosmological perturbations of quantum-mechanical origin and anisotropy of the microwave background.

Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations. PACS numbers: 98.80.Cq, 98.70.Vc, 04.30.+ Typeset using REVTEX 1 The recent discovery by COBE [1] of the angular variations of CMBR makes it necessary to analyze in greater detail the observational consequences of the quantum-mechanical generation of cosmological perturbations. The underlying physical reason for the generating process is the parametric (superadiabatic) amplification of classical perturbations and the associated quantum-mechanical particle pair creation in the variable gravitational field of the homogeneous isotropic Universe. As a result of the parametric coupling between the quantized perturbations and the variable classical “pump” field, the initial vacuum state of the perturbations evolves (in the Schrödinger picture) into a strongly squeezed vacuum state possessing very specific statistical properties. The generated fluctuations can be viewed, classically, as a stochastic collection of standing waves. The mechanism itself and its main results concerning squeezing are valid for gravitational waves and progenitors of density perturbations [2,3]. A particular variable gravitational field, that may be responsible for the amplification process, is provided by one or another type of the inflationary expansion. It is often stated that inflation generates “Gaussian perturbations with randomly distributed phases”. However, this is not the case: the phases of all modes of perturbations are essentially constant and fixed [3] which leads to standing waves, modulated spectra of the generated perturbations and a specific angular distribution of the temperature fluctuations of CMBR over the sky, as will be shown below. In this paper we will analyze, mostly, gravitational waves. For our purposes it is sufficient to consider perturbations in a spatially-flat FLRW universe ds = a(η)(dη − dx − dy − dz) where a(η) is the cosmological scale factor. The quantum-mechanical operator for the gravitational-wave field can be written in the general form