Hamiltonian Cosmological Perturbation Theory

TL;DR

This paper develops a Hamiltonian framework for cosmological perturbations in general relativity, offering new insights into the primordial power spectrum and quantum cosmological creation processes.

Contribution

It introduces a Hamiltonian perturbation theory with a novel identification of the scale factor, contrasting with traditional Lifshitz perturbations, and explores quantum creation of universes and particles.

Findings

Provides a Hamiltonian formulation of cosmological perturbations.

Offers an explanation for the primordial power spectrum.

Discusses quantum creation of universes and particles.

Abstract

The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification preserves the number of variables and leads to a cosmological perturbation theory with the scalar potential perturbations in contrast to the kinetic perturbations in the Lifshitz version which are responsible for the ``primordial power spectrum'' of CMB in the inflationary model. The Hamiltonian approach enables to explain this ``spectrum'' in terms of scale-invariant variables and to consider other topical problem of modern cosmology in the context of quantum cosmological creation of both universes and particles from the stable Bogoliubov vacuum.