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

We study the effects of Horndeski models of dark energy on the observables of the large-scale structure in the late time universe. A novel classification into Late dark energy, Early dark energy and Early modified gravity scenarios is proposed, according to whether such models predict deviations from the standard paradigm persistent at early time in the matter domination epoch. We discuss the physical imprints left by each specific class of models on the effective Newton constant µ, the gravitational slip parameter η, the light deflection parameter Σ and the growth function f σ 8 and demonstrate that a convenient way to dress a complete portrait of the viability of the Horndeski accelerating mechanism is via two, redshift-dependent, diagnostics: the µ(z) − Σ(z) and the f σ 8 (z) − Σ(z) planes. If future, model-independent, measurements point to either Σ − 1 < 0 at redshift zero or µ − 1 < 0 with Σ − 1 > 0 at high redshifts or µ − 1 > 0 with Σ − 1 < 0 at high redshifts, Horndeski theories are effectively ruled out. If f σ 8 is measured to be larger than expected in a ΛCDM model at z > 1.5 then Early dark energy models are definitely ruled out. On the opposite case, Late dark energy models are rejected by data if Σ < 1, while, if Σ > 1, only Early modifications of gravity provide a viable framework to interpret data.

We use growth of structure data to constrain the effective field theory of dark energy. Considering as case study Horndeski theories with the speed of gravitational waves equal to that of light, we show how constraints on the free parameters and the large-scale structure phenomenological functions can be improved by two ingredients: firstly by complementing the set of redshift-space distortions data with the three recent measurements of the growth rate f and the amplitude of matter fluctuations σ 8 from the VIPERS and SDSS collaborations; secondly by applying a local Solar System bound on the variation of the Newton constant. This analysis allows us to conclude that: i) despite firmly restricting the predictions of weaker gravity, the inclusion of the Solar System bound does not prevent suppressed growth relative to the standard model ΛCDM at low redshifts; ii) the same bound in conjunction with the growth of structure data strongly restricts the redshift evolution of the gravitational slip parameter to be close to unity and the present value is constrained to one at the 10 −3 level; iii) the growth of structure data favours a fifth force contribution to the effective gravitational coupling at low redshifts and at more than two sigma at present time.

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We analyse the clustering of matter on large scales in an extension of the concordance model that allows for spatial curvature. We develop a consistent approach to curvature and wide-angle effects on the galaxy 2-point correlation function in redshift space. In particular we derive the Alcock-Paczynski distortion of fσ 8, which differs significantly from empirical models in the literature. A key innovation is the use of the 'Clustering Ratio', which probes clustering in a different way to redshift-space distortions, so that their combination delivers more powerful cosmological constraints. We use this combination to constrain cosmological parameters, without CMB information. In a curved Universe, we find that Ωm, 0=0.26± 0.04 (68% CL). When the clustering probes are combined with low-redshift background probes — BAO and SNIa — we obtain a CMB-independent constraint on curvature: Ω K, 0 = 0.0041-0.0504 +0.0500. We find no Bayesian evidence that the flat concordance model can be rejected. In addition we show that the sound horizon at decoupling is r d = 144.57 ± 2.34 Mpc, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat ΛCDM and a standard sound horizon, leading to a small value of H 0, without assuming any CMB information. Clustering Ratio measurements produce the only low-redshift clustering data set that is not in disagreement with the CMB, and combining the two data sets we obtain Ω K, 0 = -0.023 ± 0.010.

Context. The key probes of the growth of a large-scale structure are its rate f and amplitude σ8. Redshift space distortions in the galaxy power spectrum allow us to measure only the combination fσ8, which can be used to constrain the standard cosmological model or alternatives. By using measurements of the galaxy-galaxy lensing cross-correlation spectrum or of the galaxy bispectrum, it is possible to break the fσ8 degeneracy and obtain separate estimates of f and σ8 from the same galaxy sample. Currently there are very few such separate measurements, but even this allows for improved constraints on cosmological models. Aims. We explore how having a larger and more precise sample of such measurements in the future could constrain further cosmological models. Methods. We considered what can be achieved by a future nominal sample that delivers an ∼1% constraint on f and σ8 separately, compared to the case with a similar precision on the combination fσ8. Results. For the six cosmological parameters of ΛCDM, we find improvements of ∼5–50% on their constraints. For modified gravity models in the Horndeski class, the improvements on these standard parameters are ∼0–15%. However, the precision on the sum of neutrino masses improves by 65% and there is a significant increase in the precision on the background and perturbation Horndeski parameters.

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