Scalar Field Oscillations Contributing to Dark Energy

We use action-angle variables to describe the basic physics of coherent scalar field oscillations in the expanding universe. These analytical mechanics methods have some advantages, like the identification of adiabatic invariants. As an application, we show some instances of potentials leading to equations of state with $p<-\rho \mathrm{/}3$, thus contributing to the dark energy that causes the observed acceleration of the universe.