Stability Properties And Asymptotics For N Nonminimally Coupled Scalar Fields Cosmology

We consider here the dynamics of some homogeneous and isotropic cosmological models with N interacting classical scalar fields nonminimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for one and two scalar fields. We show that a Lyapunov function can be constructed under certain conditions for a large class of models, suggesting that chaotic behavior is ruled out for them. Typical solutions tend generically to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic results obtained for the one field model remain valid. In particular, we confirm that, for large times and a vanishing cosmological constant, even in the presence of the extra scalar fields, the universe tends to an infinite diluted matter dominated era.42611531161Abramo, L.R., Brenig, L., Gunzig, E., Saa, A., (2003) Physical Review D: Particles and Fields, 67, p. 027301Bertolami, O., (1987) Physical Letters B, 186, p. 161Brenig, L., Figueiredo, A., Gunzig, E., Rocha Filho, T.M., Saa, A., Dynamical Study of the Singularities of Gravity in the Presence of Nonminimally Coupled Scalar Fields, , manuscript submitted for publicationDeser, S., (1984) Physical Letters B, 134, p. 419Esposito-Farese, G., Polarski, D., (2001) Physical Review D: Particles and Fields, 63, p. 063504Figueiredo, A., Rocha Filho, T.M., Gunzig, E., Brenig, L., Saa, A., (2002) International Journal of Theoretical Physics, 41, p. 2037Futamase, T., Maeda, K., (1989) Physical Review D: Particles and Fields, 39, p. 399Futamase, T., Rothman, T., Matzner, R., (1981) Physical Review D: Particles and Fields, 39, p. 405Gunzig, E., Brenig, L., Figueiredo, A., Rocha Filho, T.M., (2000) Modern Physical Letter A, 15, p. 1363Gunzig, E., Gunzig, E., Brenig, L., Faraoni, V., Rocha Filho, T.M., Figueiredo, A., (2001) International Journal of Theoretical Physics, 40, p. 2295Gunzig, E., Saa, A., Brenig, L., Faraoni, V., Rocha Filho, T.M., Figueiredo, A., (2001) Physical Review D: Particles and Fields, 63, p. 067301Hosotani, Y., (1985) Physical Review D: Particles and Fields, 32, p. 1949Starobinski, A.A., (1981) Astronomicheskii Zhurnal, 7, p. 67(1981) Soviet Astronomy Letters, 7, p. 3