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

Understand

We consider Friedmann-Lema\^{\i}tre-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.