We investigate the asymptotic behavior of the nonautonomous evolution problem
generated by the Klein-Gordon equation in an expanding background, in one space
dimension with periodic boundary conditions, with a nonlinear potential of
arbitrary polynomial growth. After constructing a suitable dynamical framework
to deal with the explicit time dependence of the energy of the solution, we
establish the existence of a regular, time-dependent global attractor. The
sections of the attractor at given times have finite fractal dimension.Comment: to appear in Discrete and Continuous Dynamical System
