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 η−dependent 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.

Squeezed states and Affleck-Dine baryogenesis

“…Using the background field method to study quantum effects [13][14][15][16], we assume field i , i ¼ 1, 2, has a background classical component i0 and a quantum (order h 2 ) field i :…”

Scalar fields and exact invariants in a Friedmann-Robertson-Walker spacetime

“…and are related to the operators b i k and b iy k by the Bogolubov transformations [17,32,33] b i k tA i k tA iy k ; (52a) b iy k tA iy k tA i k ;…”

“…In a recent article, Geralico et al [17] studied classical and quantum gravitational waves using the similarities of this problem with a damped parametric oscillator, where the mass is replaced by the square of the cosmological scale factor. In this article we investigate the quantum scalar fields in a Friedmann-Robertson-Walker (FRW) background.…”

Gaussian wave packet states of scalar fields in a universe of de Sitter

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] The study of this subject is of ultimate importance to knowledge of the scenario in the early universe. 8 As example of investigations concerning this subject we can cite those related to the determination of the vacuum expectation value of the energy-momentum tensor, 1 the problem of creation of particles in an expanding universe, [9][10][11] and the construction of squeezed quantum states.…”