Novel approach to the study of quantum effects in the early Universe
Abstract
We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function σ(η) of the conformal time η, called the auxiliary field equation. At the classical level, σ(η) can be expressed by means of two independent solutions of the “master equation” to which the perturbed Einstein equations for the gravitational waves can be reduced. At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor a^{2}(η). A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous ηdependent Hamiltonian. An estimate in terms of σ(η) and a(η) of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of η are also obtained. We conclude by discussing a few applications to quasi de Sitter and standard de Sitter scenarios.
 Publication:

Physical Review D
 Pub Date:
 February 2004
 DOI:
 10.1103/PhysRevD.69.043504
 arXiv:
 arXiv:grqc/0308039
 Bibcode:
 2004PhRvD..69d3504G
 Keywords:

 98.80.Cq;
 04.30.w;
 Particletheory and fieldtheory models of the early Universe;
 Gravitational waves: theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 20 pages, to appear on PRD. Already published background material has been either settled up in a more compact form or eliminated