Observational determination of squeezing in relic gravitational waves and primordial density perturbations

We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a nonstationary character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in the oscillatory behavior of the higher order multipoles $C_l$ of the cosmic microwave background anisotropy. We start with the gravitational wave background and then apply the theory to primordial density perturbations. We derive an analytical formula for the positions of peaks and dips in the angular power spectrum ${l(l+1\mathrm{})C}_l$ as a function of l. This formula shows that the values of l at the peak positions are ordered in the proportion $1:3:5:\dots ,$ whereas at the dips they are ordered as $1:2:3:\dots .$ We compare the derived positions with the actually observed features, and find them to be in reasonably good agreement. It appears that the observed structure is better described by our analytical formula based on the (squeezed) metric perturbations associated with the primordial density perturbations, rather than by the acoustic peaks reflecting the existence of plasma sound waves at the last scattering surface. We formulate a forecast for other features in the angular power spectrum that may be detected by the advanced observational missions, such as the Microwave Anisotropy Probe and Planck. We tentatively conclude that the observed structure is a macroscopic manifestation of squeezing in the primordial metric perturbations.