  Rather than obtaining cosmic acceleration with a scalar field potential
(quintessence) or noncanonical kinetic term (k-essence), we can do it purely
through a modified gravity braiding of the scalar and metric, i.e. the $G_3$
Horndeski action term. Such "Horndessence" allows an exact $\Lambda$CDM
cosmological expansion without any cosmological constant, and by requiring
shift symmetry we can derive the exact form of $G_3$. We find that this route
of deriving $G_3(X)$ leads to a functional form far from the usual simple
assumptions such as a power law. Horndessence without any kinetic term or
potential has the same number of parameters as $\Lambda$CDM and makes an exact
prediction for the expansion history ($\Lambda$CDM) and modified gravity cosmic
growth history; we show the viable gravitational strength $G_{\rm eff}(a)$ and
growth rate $f\sigma_8(a)$. The simplest versions of the theory fail soundness
criteria, but we learn interesting lessons along the way, in particular about
robust parametrization, and indicate possible sound extensions.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics