Since the discovery of the accelerated expansion of the Universe , the constraints on the equation of state w _ { \text { DE } } of dark energy , the stress-energy component responsible for the acceleration , have tightened significantly .
These constraints generally assume an equation of state that is slowly varying in time .
We argue that there is good theoretical motivation to consider “ monodromic ” scenarios with periodic modulations of the dark energy potential .
We provide a simple parametrization of such models , and show that these leave room for significant , periodic departures of w _ { \text { DE } } from -1 .
Moreover , simple models with non-standard kinetic term result in interesting large-scale structure phenomenology beyond that of standard slow-roll dark energy .
All these scenarios are best constrained in a dedicated search , as current analyses average over relatively wide redshift ranges .