Abstract. Large-scale structure has been shown as a promising cosmic probe for distinguishing and constraining dark energy models. Using the growth index parametrization, we obtain an analytic formula for the growth rate of structures in a coupled dark energy model in which the exchange of energy-momentum is proportional to the dark energy density. We find that the evolution of f σ 8 can be determined analytically once we know the coupling, the dark energy equation of state, the present value of the dark energy density parameter and the current mean amplitude of dark matter fluctuations. After correcting the growth function for the correspondence with the velocity field through the continuity equation in the interacting model, we use our analytic result to compare the model's predictions with large-scale structure observations.

We estimate the constraining power of J-PAS for parameters of an interacting dark energy cosmology. The survey is expected to map several millions of luminous red galaxies, emission line galaxies and quasars in an area of thousands of square degrees in the northern sky with precise photometric redshift measurements. Forecasts for the DESI and Euclid surveys are also evaluated and compared to J-PAS. With the Fisher matrix approach, we find that J-PAS can place constraints on the interaction parameter comparable to those from DESI, with an absolute uncertainty of about 0.02, when the interaction term is proportional to the dark matter energy density, and almost as good, of about 0.01, when the interaction is proportional to the dark energy density. For the equation of state of dark energy, the constraints from J-PAS are slightly better in the two cases (uncertainties 0.04-0.05 against 0.05-0.07 around the fiducial value −1). Both surveys stay behind Euclid but follow it closely, imposing comparable constraints in all specific cases considered.

The observation of galaxy and gas distributions, as well as cosmological simulations in a ΛCDM Universe, suggests that clusters of galaxies are still accreting mass and are not expected to be in equilibrium. In this work, we investigate the possibility to evaluate the departure from virial equilibrium in order to detect, in that balance, effects from a Dark Matter-Dark Energy interaction. We continue, from previous works, using a simple model of interacting dark sector, the Layzer-Irvine equation for dynamical virial evolution, and employ optical observations in order to obtain the mass profiles through weak lensing and X-ray observations giving the intracluster gas temperatures. Through a Monte Carlo method, we generate, for a set of clusters, measurements of observed virial ratios, interaction strength, rest virial ratio and departure from equilibrium factors. We found a compounded interaction strength of −1.99 +2.56 −16.00 , compatible with no interaction, but also a compounded rest virial ratio of −0.79 ± 0.13, which would entail a 2σ detection. We confirm quantitatively that clusters of galaxies are out of equilibrium but further investigation is needed to constrain a possible interaction in the dark sector.

We explore the cosmological implications of the interactions among the dark particles in the dark SU(2) R model. It turns out that the relevant interaction is between dark energy and dark matter, through a decay process. With respect to the standard Λ CDM model, it changes only the background equations. We note that the observational aspects of the model are dominated by degeneracies between the parameters that describe the process. Thus, only the usual Λ CDM parameters, such as the Hubble expansion rate and the dark energy density parameter (interpreted as the combination of the densities of the dark energy doublet) could be constrained by observations at this moment.

As the dark sector remains unknown in composition and interaction between dark energy and dark matter stand out as natural, observations of galaxy clusters out of equilibrium abound, opening a promising window on these questions. We continue here the exploration of dark sector interaction detection via clusters virial equilibrium state for all clusters configurations. The dynamics of clusters is evaluated with the Layzer-Irvine equation, a simple model of an interacting dark sector and some simplifying assumptions to obtain the time-dependent part of the virial dynamics. The clusters' data are concentrated in optical weak lensing and X-ray observations that evaluate, respectively, the clusters' mass profiles and temperatures. The global inconsistency of available X-ray data led us to constitute "gold" cluster samples. Through a Bayesian analysis, they are processed to obtain consistent interaction detected up to 3σ, in compounded interaction strength for 11 clusters at −0.027 ± 0.009 that translate in compounded universal equilibrium virial ratio of −0.61 +0.04 −0.03 . The level of detection and inconsistency of X-ray data call for caution, although future instruments promise a clearer detection soon.