  We explore a class of effective field theory models of cosmic acceleration
involving a metric and a single scalar field. These models can be obtained by
starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings
to matter satisfy the weak equivalence principle, assuming that one boson is
lighter than all the others, and integrating out the heavier fields. The result
is a quintessence model with matter coupling, together with a series of
correction terms in the action in a covariant derivative expansion, with
specific scalings for the coefficients. After eliminating higher derivative
terms and exploiting the field redefinition freedom, we show that the resulting
theory contains nine independent free functions of the scalar field when
truncated at four derivatives. This is in contrast to the four free functions
found in similar theories of single-field inflation, where matter is not
present. We discuss several different representations of the theory that can be
obtained using the field redefinition freedom. For perturbations to the
quintessence field today on subhorizon lengthscales larger than the Compton
wavelength of the heavy fields, the theory is weakly coupled and natural in the
sense of t'Hooft. The theory admits a regime where the perturbations become
modestly nonlinear, but very strong nonlinearities lie outside its domain of
validity.
