We provide explicit formulas for the effective fluid approach of f (R) theories, such as the Hu & Sawicki and the designer models. Using the latter and simple modifications to the CLASS code, which we call EFCLASS, in conjunction with very accurate analytic approximations for the background evolution, we obtain competitive results in a much simpler and less error-prone approach. We also derive the initial conditions in matter domination and we find they differ from those already found in the literature for a constant w model. A clear example is the designer model that behaves as ΛCDM in the background, but has nonetheless dark energy perturbations. We then use the aforementioned models to derive constraints from the latest cosmological data, including supernovae, BAO, CMB, H(z) and growth-rate data, and find they are statistically consistent to the ΛCDM model. Finally, we show that the viscosity parameter c 2 vis in realistic models is not constant as commonly assumed, but rather evolves significantly over several orders of magnitude, something which could affect forecasts of upcoming surveys.

Abstract. We re-analyse recent Cepheid data to estimate the Hubble parameter H 0 by using Bayesian hyper-parameters (HPs). We consider the two data sets from Riess et al 2011 and 2016 (labelled R11 and R16, with R11 containing less than half the data of R16) and include the available anchor distances (megamaser system NGC4258, detached eclipsing binary distances to LMC and M31, and MW Cepheids with parallaxes), use a weak metallicity prior and no period cut for Cepheids. We find that part of the R11 data is down-weighted by the HPs but that R16 is mostly consistent with expectations for a Gaussian distribution, meaning that there is no need to down-weight the R16 data set. For R16, we find a value of H 0 = 73.75 ± 2.11 km s −1 Mpc −1 if we use HPs for all data points (including Cepheid stars, supernovae type Ia, and the available anchor distances), which is about 2.6 σ larger than the Planck 2015 value of H 0 = 67.81±0.92 km s −1 Mpc −1 and about 3.1 σ larger than the updated Planck 2016 value 66.93 ± 0.62 km s −1 Mpc −1 . If we perfom a standard χ 2 analysis as in R16, we find H 0 = 73.46 ± 1.40 (stat) km s −1 Mpc −1 . We test the effect of different assumptions, and find that the choice of anchor distances affects the final value significantly. If we exclude the Milky Way from the anchors, then the value of H 0 decreases. We find however no evident reason to exclude the MW data. The HP method used here avoids subjective rejection criteria for outliers and offers a way to test datasets for unknown systematics.

We present a family of designer Horndeski models, i.e. models that have a background exactly equal to that of the ΛCDM model but perturbations given by the Horndeski theory. Then, we extend the effective fluid approach to Horndeski theories, providing simple analytic formulae for the equivalent dark energy effective fluid pressure, density and velocity. We implement the dark energy effective fluid formulae in our code EFCLASS, a modified version of the widely used Boltzmann solver CLASS, and compare the solution of the perturbation equations with those of the code hi CLASS which already includes Horndeski models. We find that our simple modifications to the vanilla code are accurate to the level of ∼ 0.1% with respect to the more complicated hi CLASS code. Furthermore, we study the kinetic braiding model both on and off the attractor and we find that even though the full case has a proper ΛCDM limit for large n, it is not appropriately smooth, thus causing the quasistatic approximation to break down. Finally, we focus on our designer model (HDES), which has both a smooth ΛCDM limit and well-behaved perturbations, and we use it to perform Markov Chain Monte Carlo analyses to constrain its parameters with the latest cosmological data. We find that our HDES model can also alleviate the soft 2σ tension between the growth data and Planck 18 due to a degeneracy between σ8 and one of its model parameters that indicates the deviation from the ΛCDM model.

We demonstrate the importance of including the lensing contribution in galaxy clustering analyses with large galaxy redshift surveys. It is well known that radial cross-correlations between different redshift bins of galaxy surveys are dominated by lensing. But we show here that also neglecting lensing in the autocorrelations within one bin severely biases cosmological parameter estimation with redshift surveys. It leads to significant shifts for several cosmological parameters, most notably the scalar spectral index and the neutrino mass scale. Especially the latter parameter is one of the main targets of future galaxy surveys.

We study a new model of scalar field with a general non-minimal kinetic cou- 95.36+x, 04.50.kd

We study a dark energy model with non-zero anisotropic stress, either linked to the dark energy density or to the dark matter density. We compute approximate solutions that allow to characterise the behaviour of the dark energy model and to assess the stability of the perturbations. We also determine the current limits on such an anisotropic stress from the cosmic microwave background data by the Planck satellite, and derive the corresponding constraints on the modified growth parameters like the growth index, the effective Newton's constant and the gravitational slip.

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We study the age problem of the universe with the holographic DE model introduced in [21], and test the model with some known old high redshift objects (OHRO). The parameters of the model have been constrained using the SNIa, CMB and BAO data set. We found that the age of the old quasar APM 08 279+5255 at z = 3.91 can be described by the model. PACS: 98.80.-k, 95.36.+x 1 Introduction The astrophysical data from distant Ia supernovae observations [1], [2], cosmic microwave background anisotropy [3], and large scale galaxy surveys [4], [5], all indicate that the current Universe is not only expanding, it is accelerating due to some kind of negative-pressure form of matter known as dark energy ([6],[7],[8], [9]). The combined analysis of cosmological observations also suggests that the universe is spatially flat, and consists of about ∼ 1/3 of dark matter (the known baryonic and nonbaryonic *