2.a Perturbation Theory of the Gravitational Field

The perturbation theory of the gravitational field aims to study the stability of homogeneous and isotropic cosmological models of the type Friedmann-Lemaitre-Robertson-Walker (FLRW). The main novelty in our approach to this problem is the use of Quasi-Maxwellian equations which have been studied by our group in, e.g., M.Novello e J.M.Salim, Fundamentals of Cosmic Physics 8, 201, 1983 and J.M.Salim Ph. D. thesis, "Quasi-Maxwellian Equations of Gravitation: Applications to the Friedmann Universe - CBPF, 1982). The Quasi-Maxwellian equations yields naturally a gauge invariant formalism based on obsevable quantities with a simple interpretation. This formalism also yieds a compact treatment of the perturbations based on a hamiltonian dynamical system (see M. Novello, J.M.Salim, M.C.Motta da Silva, S.E.Jorás e R.Klippert, Physical Review D 51, 2, 450, 1995 - M.Novello, J.M.Salim, M.C.Motta da Silva, S.E.Jorás e R.Klippert, Physical Review D 52, 2 750, 1995 - M.Novello, J.M.Salim, M.C.Motta da Silva e R.Klippert, Physical Review D 54, 4, 2578, 1996). A quantum analysis was also done in M.Novello, J.M.Salim, M.C.Motta da Silva e R.Klippert, Physical Review D 54, 10, 1996. As a first result we obtained squeezed states for gravitational waves (M.Novello, J.M.Salim, M.C.Motta da Silva e R.Klippert. Physical Review D 54, 4, 2578, 1996)., in accordance with other authors. We intend to use this treatment to examine sqeezed states of the electromagnetic field non minimally coupled to the gravitational field in an expanding universe. We are now developing this formalism in order to compare with COBE, Boomerang and Maxima observations. We are also investigating the application of this gauge-invariant method to the treatment of perturbations in anisotropic cosmological models like Bianchi-I and Gödel (see M.Novello, J.M.Salim, M.C.Motta da Silva e R.Klippert, Physical Review D 61, 124025-1 - 124025-19, 2000 e R.Klippert, Ph.D. thesis, CBPF, 1998, respectively). An analysis for models with rotation using Gödel?s model as a paradigm) is under development.

Another line of research related to the one described here is the Quantum theory of Cosmological perturbations. We seek in this case to quantize the results obtained previously for a Friedmann-Robertson-Walker model. A result has already been published: we showed (M.Novello, J.M.Salim, M.C.Motta da Silva e R.Klippert. Physical Review D 54, 4, 2578, 1996) the existence of squeezed states in the gravitational waves, in agreement with other authors. We want to proceed with the study of squeezed states of electromagnetic nature, via a nonminimal coupling with gravity, in an expanding universe.