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

Testing deviations from Lambda CDM with growth rate measurements from six large-scale structure surveys at z=0.06-1

We use measurements from the Planck satellite mission and galaxy redshift surveys over the last decade to test three of the basic assumptions of the standard model of cosmology, $\Lambda$CDM: the spatial curvature of the universe, the nature of dark energy and the laws of gravity on large scales. We obtain improved constraints on several scenarios that violate one or more of these assumptions. We measure $w_0=-0.94\pm0.17$ (18\% measurement) and $1+w_a=1.16\pm0.36$ (31\% measurement) for models with a time-dependent equation of state, which is an improvement over current best constraints \citep{Aubourg2014}. In the context of modified gravity, we consider popular scalar tensor models as well as a parametrization of the growth factor. In the case of one-parameter $f(R)$ gravity models with a $\Lambda$CDM background, we constrain $B_0 < 1.36 \times 10^{-5}$ (1$\sigma$ C.L.), which is an improvement by a factor of 4 on the current best \citep{XU2015}. We provide the very first constraint on the coupling parameters of general scalar-tensor theory and stringent constraint on the only free coupling parameter of Chameleon models. We also derive constraints on extended Chameleon models, improving the constraint on the coupling by a factor of 6 on the current best \citep{Hojjati2011} . We also measure $\gamma = 0.612 \pm 0.072$ (11.7\% measurement) for growth index parametrization. We improve all the current constraints by combining results from various galaxy redshift surveys in a coherent way, which includes a careful treatment of scale-dependence introduced by modified gravity.Comment: citation updates, 13 pages, 13 figures (submitted to MNRAS) , video summary on youtube: https://www.youtube.com/watch?v=xvDO2cySQnw&feature=youtu.b

Improvements in cosmological constraints from breaking growth degeneracy

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

Extending cosmological tests of General Relativity with the Square Kilometre Array

Tests of general relativity (GR) are still in their infancy on cosmological scales, but forthcoming experiments promise to greatly improve their precision over a wide range of distance scales and redshifts. One such experiment, the Square Kilometre Array (SKA), will carry out several wide and deep surveys of resolved and unresolved neutral hydrogen (H i) 21 cm line-emitting galaxies, mapping a significant fraction of the sky from $0\leqslant z\lesssim 6$. I present forecasts for the ability of a suite of possible SKA H i surveys to detect deviations from GR by reconstructing the cosmic expansion and growth history. SKA Phase 1 intensity mapping surveys can achieve sub-1% measurements of $f{\sigma }_{8}$ out to $z\approx 1$, with an SKA1-MID Band 2 survey out to z lesssim 0.6 able to surpass contemporary spectroscopic galaxy surveys such as DESI and Euclid in terms of constraints on modified gravity parameters if challenges such as foreground contamination can be tackled effectively. A more futuristic Phase 2 H i survey of $\sim {10}^{9}$ spectroscopic galaxy redshifts would be capable of detecting a $\sim 2\%$ modification of the Poisson equation out to z ≈ 2

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