We present a systematic study of modified gravity (MG) models containing a single scalar field non-minimally coupled to the metric. Despite a large parameter space, exploiting the effective field theory of dark energy (EFT of DE) formulation and imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions about the large scale structures.The goal of this work, in collaboration with F. Piazza, C. Marinoni and L. Hui 1 , is to study the predictability of MG theories aiming at challenging the standard ΛCDM explanation of cosmic acceleration. We use the EFT of DE 2 for it has established a common formalism to describe the widest set of MG theories, those adding a single extra scalar degree of freedom to the Einstein-Hilbert action.Such a unifying description enables MG theories to be parametrized in a common framework in terms of structural functions of time, describing how matter perturbations evolve in the universe. The requirements needed to fully describe an EFT model can be reduced to two constants and three functions of time Ω 0 m , w, µ(t), µ 3 (t), 4 (t) . The three functions are nonminimal couplings, once "turned on" they enable the description theories in the Horndeski class: µ is the Brans-Dicke (BD) non-minimal coupling, adding µ 3 models the cubic galileon (H3 ) term and 4 encodes the 4 and 5 Horndeski (H45 ) Lagrangians. In parallel, the EFT of DE allows one to independently set the background expansion, i.e the Hubble rate. This reduces to fixing the two constants, the present fractional matter density of non-relativistic matter in the perfect fluid approximation Ω 0 m and the background DE equation of state parameter w 3 . They are set by the latest constraints 4 to reproduce a flat ΛCDM background, thus respectively ∼ 0.3 and −1.Another asset of the EFT of DE is to provide a clear and common means of assessing if theories are pathological or not, i.e whether they suffer from ghost or gradient instabilities. The main purposes of this work is to show that despite large degrees of freedom, definite features common to all healthy -stable and with no superluminal propagation of scalar and tensor modes-EFT models arise within the vast Horndeski class. We show this by expanding the non-minimal coupling functions in power series up to second order in the reduced matter density, x, used as time variable. An overall (1 − x) pre-factor ensures the vanishing of the couplings at early times, hence recovering general relativity. We randomly generate the coefficients of the expansions until we obtain 10 4 healthy BD, H3 and H45 theories. a Proceedings of 51st Rencontres de Moriond arXiv:1607.06916v1 [astro-ph.CO]

The discovery of cosmic acceleration has triggered a consistent body of theoretical work aimed at modeling its phenomenology and understanding its fundamental physical nature. In recent years, a powerful formalism that accomplishes both these goals has been developed, the so-called effective field theory of dark energy. It can capture the behavior of a wide class of modified gravity theories and classify them according to the imprints they leave on the smooth background expansion history of the Universe and on the evolution of linear perturbations. The effective field theory of dark energy is based on a Lagrangian description of cosmological perturbations which depends on a number of functions of time, some of which are non-minimal couplings representing genuine deviations from standard gravity. Such a formalism is thus particularly convenient to fit and interpret the wealth of new data that will be provided by future galaxy surveys. Despite its recent appearance, this formalism has already allowed a systematic investigation of what lies beyond the standard gravity landscape and provided a conspicuous amount of theoretical predictions and observational results. In this review, we report on these achievements. Conclusion and outlook 94Appendix A Acronyms and symbols 971. Scalar-tensor theoriesà la Brans-Dicke, hereafter dubbed Generalized