Scalar-tensor cosmologies with a potential in the general relativity limit Time evolution

We consider Friedmann-Lemaitre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity The latter can be subsumed under two types (i) exponential convergence and (ii) damped oscillations around general relativity As an illustration we present an example of oscillating dark energy (C) 2010 Elsevier B V All rights reserved