Phenomenology of dark energy: exploring the space of theories with
  future redshift surveys
  We use the effective field theory of dark energy to explore the space of
modified gravity models which are capable of driving the present cosmic
acceleration. We identify five universal functions of cosmic time that are
enough to describe a wide range of theories containing a single scalar degree
of freedom in addition to the metric. The first function (the effective
equation of state) uniquely controls the expansion history of the universe. The
remaining four functions appear in the linear cosmological perturbation
equations, but only three of them regulate the growth history of large scale
structures. We propose a specific parameterization of such functions in terms
of characteristic coefficients that serve as coordinates in the space of
modified gravity theories and can be effectively constrained by the next
generation of cosmological experiments. We address in full generality the
problem of the soundness of the theory against ghost-like and gradient
instabilities and show how the space of non-pathological models shrinks when a
more negative equation of state parameter is considered. This analysis allows
us to locate a large class of stable theories that violate the null energy
condition (i.e. super-acceleration models) and to recover, as particular
subsets, various models considered so far. Finally, under the assumption that
the true underlying cosmological model is the $\Lambda$ Cold Dark Matter
($\Lambda$CDM) scenario, and relying on the figure of merit of EUCLID-like
observations, we demonstrate that the theoretical requirement of stability
significantly narrows the empirical likelihood, increasing the discriminatory
power of data. We also find that the vast majority of these non-pathological
theories generating the same expansion history as the $\Lambda$CDM model
predict a different, lower, growth rate of cosmic structures.
