Initial Conditions for Non-Canonical Inflation

We investigate the dynamics of homogeneous phase space for single-field models of inflation. Inflationary trajectories are formally attractors in phase space, but since in practice not all initial conditions lead to them, some degree of fine tuning is required for successful inflation. We explore how the dynamics of non-canonical inflation, which has additional kinetic terms that are powers of the kinetic energy, can play a role in ameliorating the initial conditions fine tuning problem. We present a qualitative analysis of inflationary phase space based on the dynamical behavior of the scalar field. This allows us to construct the flow of trajectories, finding that trajectories generically decay towards the inflationary solution at a steeper angle for non-canonical kinetic terms, in comparison to canonical kinetic terms, so that a larger fraction of the initial-conditions space leads to inflation. Thus, non-canonical kinetic terms can be important for removing the initial conditions fine-tuning problem of some small-field inflation models.