## Phenomenology of dark energy: exploring the space of theories with future redshift surveys

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Abstract: We use the effective field theory of dark energy to explore the space of modified gravitymodels which are capable of driving the present cosmic acceleration. We identify five universal functions of cosmic time, which 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 shrinkswhen 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 scenario, and relying on the figure of merit with which relevant observables of the model will be constrained by future experiments, we demonstrate that the space spanned by stable gravitational theories that will not be statistically rejected by data is actually much smaller than the space enclosed by the likelihood contours.