MG12 - Talk detail
 

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Abstract

CMB Polarization Generated by Primordial Gravitational Waves. Analytical solutions.

The problem is reduced to the single integral equation presented in the operator form written in terms of relevant integral and differential operators. It is shown that in the low frequency limit the integral equation can be presented in terms of integral operators only and an analytical expansion over frequencies is obtained. Then it is shown that in the high frequency limit the integral equation can be presented in terms of differential operators only and an asymptotic solution is found. The problem of resonance generation of polarization is discussed.

The Problem of Initial Conditions for Primordial Black Hole Formation and Asymptotic Quasi-Homogeneous Solution.

According to the asymptotic quasi-homogeneous solution near a cosmological singularity an arbitrary curvature profile does not depend on time, while perturbations of energy density and velocity vanish asymptotically at the singularity. The asymptotic quasi-homogeneous solutions of the first and second order are used to set self-consistent initial conditions for subsequent numerical simulations of primordial black hole formation.

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