STABILITY OF FRW COSMOLOGY IN HIGHER-ORDER GRAVITY

We analyze the behavior of radiation-filled, homogeneous, and isotropi c cosmological solutions to a generalized higher order gravity theory which is derived from a gravitational Lagrangian that is an arbitrary function of the scalar spacetime curvature f (R). We give necessary an d sufficient conditions for the existence and stability of general rel ativistic sigma=+/-1,0 FRW solutions with in this general theory. We s how that under some general conditions any homogeneous and isotropic s olution of general relativity is also an exact solution of the f (R) t heory, and every radiation solution (not necessarily isotropic) in gen eral relativity is an exact solution in higher order gravity provided there are no nonzero constants and the Einstein term is present in the gravitational Lagrangian of our theory. We then prove that nonflat FR W solutions of general relativity are generically unstable and so do n ot approach the corresponding ones in higher order gravity for large t imes. This may be interpreted as an indication that homogeneous and is otropic solutions of higher order gravity cannot be obtained from the corresponding nonflat FRW solutions of general relativity via perturba tion theory. However, we find a stable regime for flat FRW solutions o f general relativity in higher order gravity. In particular, under fai rly general circumstances, flat FRW solutions of general relativity ar e stable against homogeneous and isotropic perturbations in higher ord er gravity and always approach their corresponding ones in the general ized theory at the large time limit. The requirements for stability of the flat FRW solutions in higher order gravity coincide with well-kno wn constraints for the absence of tachyons and the existence of comple x instanton solutions in the theory, and are exactly those needed to p roduce bouncing, regular solutions on approach to the singularity.