Global dynamics and inflationary center manifold and slow-roll approximants

Understand

We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lema\^itre-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of scalar field potentials and problems in e.g.

• modified gravity.
• We present a global and regular dynamical systems description that yields a global understanding of the solution space, including asymptotic features.
• We introduce dynamical systems techniques such as center manifold expansions and use Pad\'e approximants to obtain improved approximations for the `attractor solution' at early times.