Horndessence: $\Lambda$CDM Cosmology from Modified Gravity
  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.
