I give a brief review of the status of research on the nature of initial conditions required to
obtain a period of cosmological inflation. It is shown that there is good evidence that in the …

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field
in 3+ 1 dimensions, we study the conditions under which a universe that is initially …

We consider the effects of inhomogeneous initial conditions in both the scalar field profile
and the extrinsic curvature on different inflationary models. In particular, we compare the …

Inflationary α-attractor models in supergravity, which provide excellent fits to the latest
observational data, are based on the Poincaré disk hyperbolic geometry. We refine these …

A bstract Inflationary spacetimes have been argued to be past geodesically incomplete in
many situations. However, whether the geodesic incompleteness implies the existence of an …

Inflation is considered as the best theory of the early universe by a very large fraction of
cosmologists. However, the validity of a scientific model is not decided by counting the …

In this review, a pedagogical introduction to the concepts of slow-roll inflationary universe
and number of e-folds is provided. In particular, the differences between the basic notion of …

We study the robustness of single-field inflation against inhomogeneities. We derive a
simple analytic criterion on the shape of the potential for successful inflation in the presence …

Extending our previous work on the robustness of inflation to perturbations in the scalar field,
we investigate the effects of perturbations in the transverse traceless part of the extrinsic …

We use the 3+ 1 formalism of numerical relativity to investigate the robustness of Starobinsky
and Higgs inflation to inhomogeneous initial conditions, in the form of either a field gradient …