Kinetic initial conditions for inflation

We consider the classical evolution of the inflaton field φ(t) and the Hubble parameter $H(t)$ in homogeneous and isotropic single-field inflation models. Under an extremely broad assumption, we show that the Universe generically emerges from an initial singularity in a noninflating state where the kinetic energy of the inflaton dominates its potential energy, .φ²V(φ). In this kinetically dominated regime, the dynamical equations admit simple analytic solutions for φ(t) and $H(t)$, which are independent of the form of V(φ). In such models, these analytic solutions thus provide a simple way of setting the initial conditions from which to start the (usually numerical) integration of the coupled equations of motion for φ(t) and $H(t)$. We illustrate this procedure by applying it to spatially flat models with polynomial and exponential potentials, and determine the background evolution in each case; generically $H(t)$ and |φ(t)| as well as their time derivatives decrease during kinetic dominance until .φ²~V(φ), marking the onset of a brief period of fast-roll inflation prior to a slow-roll phase. We also calculate the approximate spectrum of scalar perturbations produced in each model and show that it exhibits a generic damping of power on large scales. This may be relevant to the apparent low- falloff in the cosmic microwave background power spectrum.