ASYMPTOTIC STATES OF GENERALIZED UNIVERSES WITH HIGHER DERIVATIVES

Abstract

We review ongoing research related to the asymptotic dynamics of isotropic universes in theories with higher derivatives, especially near the initial singularity. We treat two major cases, that is universes in vacuum, and also those filled with radiation using the method of asymptotic splittings of vector fields. Our solutions have the form of formal Fuchsian-type series for the basic unknowns and are valid near collapse or big rip regimes asymptotically. Isotropic universes in vacuum or those filled with radiation have always been primary examples in efforts to model the effects of higher derivative terms near extreme conditions and cosmological singularities, cf. Refs. [1], [2], [3]. With the advent of newer and more powerful mathematical methods to study the asymptotic structure of dynamical systems of Refs. [4, 5], there is now the prospect of understanding the possible effects near spacetime singularities in a deeper and more complete and transparent way. Radiation-filled universes in gravity theories with higher derivatives have been analyzed in this way in Refs. [6, 7], in an effort to understand their dynamics near the initial cosmological singularity. The general higher order action is S = 1