  We investigate cosmological models in which dynamical dark energy consists of
a scalar field whose present-day value is controlled by a coupling to the
neutrino sector. The behaviour of the scalar field depends on three functions:
a kinetic function, the scalar field potential, and the scalar field-neutrino
coupling function. We present an analytic treatment of the background evolution
during radiation- and matter-domination for exponential and inverse power law
potentials, and find a relaxation of constraints compared to previous work on
the amount of early dark energy in the exponential case. We then carry out a
numerical analysis of the background cosmology for both types of potential and
various illustrative choices of the kinetic and coupling functions. By applying
bounds from Planck on the amount of early dark energy, we are able to constrain
the magnitude of the kinetic function at early times.
