Inflaton Dynamics in Higher-Derivative Scalar-Tensor Theories of Gravity

During inflation, higher derivative terms in the gravitational action may play a significant role. Building on new stable formulations of four-derivative scalar-tensor theories, we study the impact of these corrections in the case where the inflaton is also the additional scalar degree of freedom of the modified theory. This case is highly restricted by requiring that in the homogeneous limit inflation must still work, and that the initial data must be in the weak coupling limit to respect the validity of the effective theory. In such cases, the non-linear dynamics of large perturbations are very similar to the GR case, with the main deviations captured by the terms relating to the homogeneous Einstein-scalar-Gauss-Bonnet contributions. We show that in principle it is possible to dynamically drive the field out of the weak-coupling regime from a starting point well within it, but that to do so one has to finely tune the setup, so such cases are unlikely to occur generically. This work provides a basis for the study of less restricted models in future, for example those in which the inflaton and scalar degree of freedom are independent, or in which one is not restricted to a weakly coupled regime.