Sam E. Brady

A key question in early Universe cosmology is whether inflation can be successfully seeded by a generic, localized fluctuation in the inflaton field that probes the inflationary part of the potential. Past simulations have mainly considered periodic spacetimes representing either a closed universe of a specific size or a typical patch of a larger one, and as a result have needed to impose restrictive conditions on the extrinsic and intrinsic curvatures, which are arguably not generic. In this work we consider initial fluctuations in asymptotically flat spacetimes, allowing more general profiles of the intrinsic and extrinsic curvature. Our findings confirm and generalise the result of Goldwirth and Piran that a fluctuation with proper size several times the inflationary scale 1 / G ρ infl is required for successful inflation. We also discuss inherent restrictions on the initial data, and how imposing a periodic length close to the inflationary scale may bias results.

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.

Modified gravity theories such as Einstein scalar Gauss Bonnet contain higher-derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In principle, such modifications may affect the principal part of the operator in the resulting elliptic equations, and so further complicate the already highly nonlinear, coupled constraints that apply to the initial data in numerical relativity simulations of curved spacetimes. However, since these are effective field theories, we expect the additional curvature terms to be small, which motivates treating them simply as an additional source in the constraints, and iterating to find a solution to the full problem. In this work we implement and test a modification to the CTT/CTTK methods of solving the constraints for the case of the most general four derivative, parity invariant scalar-tensor theory, and show that solutions can be found in both asymptotically flat/black hole and periodic/cosmological spacetimes, even up to couplings of order unity in the theory. Such methods will allow for numerical investigations of a much broader class of initial data than has previously been possible in these theories, and should be straightforward to extend to similar models in the Horndeski class.