Quadratic Lagrangians and horizons

Details Quadratic Lagrangians and horizons Quadratic Lagrangians and horizons

Nov 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..44.3087r&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 44, Issue 10, 15 November 1991, pp.3087-3095

Mathematics

Logic

3

Scientific paper

It has been known for some time that the standard isotropic cosmological model with an R2 Lagrangian has horizon-breaking solutions in the t-->0 singularity limit. We search for horizonless power-law solutions in the vacuum Bianchi type-I and orthogonal type-V cosmological models. We find that type V with an R2 Lagrangian does contain such solutions. At first glance this would suggest that quadratic theories might provide an alternative resolution to the horizon problem. However, for both the horizonless isotropic and type-V solutions we show that the eigenvalues of the linear vector field near the stationary points in phase space have opposite signs, demonstrating that such solutions are not Lyapunov stable. The addition of free quantum fields may stabilize the solutions.

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