Kinetic Initial Conditions for Inflation

Understand

We consider the classical evolution of the inflaton field $\phi(t)$ 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 non-inflating state where the kinetic energy of the inflaton dominates its potential energy, $\dot{\phi}^2 \gg V(\phi)$.
• In this kinetically-dominated regime, the dynamical equations admit simple analytic solutions for $\phi(t)$ and $H(t)$, which are independent of the form of $V(\phi)$.
• 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 $\phi(t)$ and $H(t)$.