A flat Friedman-Roberson-Walker universe dominated by a cosmological constant (Λ) and cold dark matter (CDM) has been the working model preferred by cosmologists since the discovery of cosmic acceleration 1, 2 . However, tensions of various degrees of significance are known to be present among existing datasets within the ΛCDM framework [3][4][5][6][7][8][9][10][11] . In particular, the Lyman-α forest measurement of the Baryon Acoustic Oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey (BOSS) 3 prefers a smaller value of the matter density fraction Ω M compared to the value preferred by cosmic microwave background (CMB The observational datasets considered in this work include the latest CMB temperature and polarisation anisotropy spectra, the supernovae (SNe) luminosity distance data, the BAO angular diameter distance data from the clustering of galaxies (gBAO) and from the Lyman-α forest (LyαFB), the measurement of H 0 , H(z) measurements using the relative age of old and passively evolving galaxies (OHD), the three-dimensional galaxy power spectra, and the two-dimensional weak lensing shear angular power spectra. Further details about the datasets and associated systematic effects can be found in Methods.The KL divergence, also known as relative entropy, quantifies the proximity of two probability density functions (PDFs). Rather than focusing on particular model parameters, it is designed to compare the overall concordance of datasets within a given model. We use the difference between the actual and the expected KL divergence, called "Surprise" 15 , as a measure of tension between datasets. Rather than comparing the PDFs for the ΛCDM parameters for every pair of datasets, we take the combined dataset, ALL16 (see Supplementary Fig. 1b), with the first two values signalling significant tension.Next, we check if the tension within the ΛCDM model can be interpreted as evidence for a dynamical DE. The dynamics of DE can be probed in terms of its equation of state w, which is equal to −1 for Λ, but is different in dynamical DE models where it will generally be a function of redshift z. Commonly considered alternatives to Λ are a model with a constant w (wCDM), and one in which w is linear function of the scale factor (w 0 w a CDM) 16 . We allow for a general evolution of the DE equation of state and use the correlated prior method 17 to perform a Bayesian non-parametric reconstruction of w(z) using the Monte Carlo Markov Chain method with other cosmological parameters marginalised over (see Methods for details). 0 during matter domination. Such dynamics would be consistent with our reconstruction and could be tested in the future when BAO measurements at higher redshifts become available. In addition to the reconstruction from the combined ALL16 dataset presented in Fig. 2, we present reconstructions derived from ten different data combinations in Supplementary Fig. 1.The results for tension between datasets, re-evaluated for the ALL 16 best fit w(z)CDM model, are shown with dark blue bars in F...

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Abstract:The Horizon Run 4 is a cosmological N -body simulation designed for the study of coupled evolution between galaxies and large-scale structures of the Universe, and for the test of galaxy formation models. Using 6300 3 gravitating particles in a cubic box of L box = 3150 h −1 Mpc, we build a dense forest of halo merger trees to trace the halo merger history with a halo mass resolution scale down to M s = 2.7 × 10 11 h −1 M ⊙ . We build a set of particle and halo data, which can serve as testbeds for comparison of cosmological models and gravitational theories with observations. We find that the FoF halo mass function shows a substantial deviation from the universal form with tangible redshift evolution of amplitude and shape. At higher redshifts, the amplitude of the mass function is lower, and the functional form is shifted toward larger values of ln(1/σ). We also find that the baryonic acoustic oscillation feature in the two-point correlation function of mock galaxies becomes broader with a peak position moving to smaller scales and the peak amplitude decreasing for increasing directional cosine µ compared to the linear predictions. From the halo merger trees built from halo data at 75 redshifts, we measure the half-mass epoch of halos and find that less massive halos tend to reach half of their current mass at higher redshifts. Simulation outputs including snapshot data, past lightcone space data, and halo merger data are available at http://sdss.kias.re.kr/astro/Horizon-Run4 .

Using measurements of H(z) and d A (z) from the Baryon Oscillation Spectroscopic Survey (BOSS) DR12 and luminosity distances from the Joint Lightcurve Analysis (JLA) compilation of supernovae (SN), we measure H 0 r d without any model assumption. Our measurement of H 0 r d = (10 033.20 +333.10 −371.81 (SN)±128.19 (BAO)) km s −1 is consistent with Planck constrains for the flat ΛCDM model. We also report that higher expansion history rates h(z) (among the possibilities) as well as lower-bound values of H 0 r d result in better internal consistency among the independent data (H(z)r d and d A (z)/r d from BAO at z = 0.32 and z = 0.57 and d L from JLA) we used in this work. This can be interpreted as an interesting and independent support of Planck cosmology without using any cosmic microwave background data. We then combine these observables to test the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and the flatness of the Universe in a model-independent way at two redshifts, namely 0.32 and 0.57, by introducing a new diagnostic for flat-FLRW, Θ(z), which only depends on observables of BAO and SN data. Our results are consistent with a flat-FLRW Universe within 2σ.

We combine model-independent reconstructions of the expansion history from the latest Pantheon supernovae distance modulus compilation and measurements from baryon acoustic oscillation to test some important aspects of the concordance model of cosmology namely the FLRW metric and flatness of spatial curvature. We then use the reconstructed expansion histories to fit growth measurement from redshift-space distortion and obtain constraints on (Ωm, γ, σ8) in a model independent manner. Our results show consistency with a spatially flat FLRW Universe with general relativity to govern the perturbation in the structure formation and the cosmological constant as dark energy. However, we can also see some hints of tension among different observations within the context of the concordance model related to high redshift observations (z > 1) of the expansion history. This supports earlier findings of [1,2] and highlights the importance of precise measurement of expansion history and growth of structure at high redshifts.