Particle creation in some LRS Bianchi I models

Abstract

Quantum effects of the gravitational field are one of the greatest mysteries of nature; having a quantum theory of gravity would be one of the greatest achievements of modern science. However, we do not currently have a satisfactory theory of the quantum nature of the gravitational field that can describe and explaining the various scenarios of the very early universe. Although we do not have a satisfactory quantum gravity theory, there is no impediment to develop quantum field theory in non-flat space-time; quantum field theory can be developed including gravitational fields without a quantum theory of gravity,using a classical gravitational field, i.e. one given as a Lorentzian metric that is a solution of Einstein’s equations. The scheme is a theory describing the dynamics of quantum fields propagating in a curved spacetime background, described by a Lorentzian manifold with a general classical metric gμν . In this way it is possible to go quite far in generalizing quantum field theory without considering the difficulties and problems involved in any quantum field theory of gravity. The Unruh effect, Hawking radiation, the production of particles in the early universe, the generation of primordial gravitational waves or even the explanation of the isotropy of the universe are some consequences of the quantum field theory in curved space-time. Particle production from vacuum is one of the most amazing predictions of quantum theory; in curved space-time, production takes place because of very intense or changing gravitational fields such as the expansion of the universe, an effect Schrödinger expected to occur [1], or the field produced by a black hole, effect studied by Hawking [2]. Parker’s pioneering works [3–5] establishes that there is a creation of particles in the very early stages of the expansion of the universe; if this particle creation at very early times is characterized by the fundamental constants ~ , c , G , then is consistent with the entropy demanded by the cosmic background radiation with a temperature of 2, 7 K [6, 7]. The majority of the works on particle production deal with the production of particles in homogeneous and isotropic universes without initial singularity in t = 0, for example, De Sitter’s universe [8], models of Friedman-Robertson-Walker [9, 10] or models of an asymptotically flat universe [11]; very few works discuss the production of particles in homogeneous anisotropic universes with initial singularity. The reason for this is partly that the usual techniques of quantum field theory in gravitational backgrounds fail when there is an initial singularity, so a different approach must be taken. The different methods that exist to address this problem are