Diagnostic of Horndeski Theories

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 {\it Late dark energy}, {\it Early dark energy} and {\it 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 $\mu$, the gravitational slip parameter $\eta$, the light deflection parameter $\Sigma$ and the growth function $f\sigma_8$ 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 $\mu(z)-\Sigma(z)$ and the $f\sigma_8(z)-\Sigma(z)$ planes. If future, model-independent, measurements point to either $\Sigma-10$ at high redshifts or $\mu-1>0$ with $\Sigma-1<0$ at high redshifts, Horndeski theories are effectively ruled out. If $f\sigma_8$ is measured to be larger than expected in a $\Lambda$CDM 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 $\Sigma1$, only Early modifications of gravity provide a viable framework to interpret data

Phenomenology of dark energy: general features of large-scale perturbations

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ - the ratio of the space part of the metric perturbation to the time part - is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.Comment: 24 pages, 7 figure

Measuring dark energy with expansion and growth

We combine cosmic chronometer and growth of structure data to derive the redshift evolution of the dark energy equation of state $w$, using a novel agnostic approach. The background and perturbation equations lead to two expressions for $w$, one purely background-based and the other relying also on the growth rate of large-scale structure. We compare the features and performance of the growth-based $w$ to the background $w$, using Gaussian Processes for the reconstructions. We find that current data is not precise enough for robust reconstruction of the two forms of $w$. By using mock data expected from next-generation surveys, we show that the reconstructions will be robust enough and that the growth-based $w$ will out-perform the background $w$. Furthermore, any disagreement between the two forms of $w$ will provide a new test for deviations from the standard model of cosmology.Comment: 10 pages, 6 figures. Version accepted in Physics of the Dark Univers

Eléments de phénoménologie de l'énergie sombre

The ΛCDM paradigm is the standard model of cosmology. In this model, the universe is constituted today for the major part by Cold Dark Matter along with the Cosmological Constant Λ that drives cosmic acceleration. However, this standard model is not fully complete. Using the Cosmological Constant introduces theoretical issues in a quantum field theory description and tentative observational evidences suggests our large scale description of the universe should be refined. Finding alternatives to the standard model is therefore of crucial importance today.Le paradigme ΛCDM est le modèle standard de la cosmologie. Dans ce modèle, l'univers est constitué aujourd'hui en majeure partie par de la matière noire froide (CDM) et la constante cosmologique Λ qui produit l'accélération cosmique. Cependant, ce modèle standard n'est pas entièrement complet. L'utilisation de la constante cosmologique introduit des problèmes théoriques dans une description de la théorie des champs quantiques et des indications observationnelles suggèrent que notre description à grande échelle de l'univers devrait être affinée. Ainsi, trouver des alternatives au modèle standard est d'une importance cruciale aujourd'hui

Eléments de phénoménologie de l'énergie sombre

The ΛCDM paradigm is the standard model of cosmology. In this model, the universe is constituted today for the major part by Cold Dark Matter along with the Cosmological Constant Λ that drives cosmic acceleration. However, this standard model is not fully complete. Using the Cosmological Constant introduces theoretical issues in a quantum field theory description and tentative observational evidences suggests our large scale description of the universe should be refined. Finding alternatives to the standard model is therefore of crucial importance today.Le paradigme ΛCDM est le modèle standard de la cosmologie. Dans ce modèle, l'univers est constitué aujourd'hui en majeure partie par de la matière noire froide (CDM) et la constante cosmologique Λ qui produit l'accélération cosmique. Cependant, ce modèle standard n'est pas entièrement complet. L'utilisation de la constante cosmologique introduit des problèmes théoriques dans une description de la théorie des champs quantiques et des indications observationnelles suggèrent que notre description à grande échelle de l'univers devrait être affinée. Ainsi, trouver des alternatives au modèle standard est d'une importance cruciale aujourd'hui

Effective Field Theory of Dark Energy: a Review

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

Effective field theory of dark energy: A review

International audienceThe 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 General Relativity. 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 General Relativity landscape and provided a conspicuous amount of theoretical predictions and observational results. In this review, we report on these achievements

Opinion et projet de loi sur la responsabilité des ministres et de tous leurs agents, adressés à MM. les Députés, MM. les Pairs, et à l'Europe entière, par un Français qui a toujours été libre. [Signé : P*. L*. M*. (Louis-Marie Perenon.)]

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