We study the large-scale anisotropy of the universe by measuring the dipole in the angular distribution of a flux-limited, all-sky sample of 1.36 million quasars observed by the Wide-field Infrared Survey Explorer (WISE). This sample is derived from the new CatWISE2020 catalog, which contains deep photometric measurements at 3.4 and 4.6 μm from the cryogenic, post-cryogenic, and reactivation phases of the WISE mission. While the direction of the dipole in the quasar sky is similar to that of the cosmic microwave background (CMB), its amplitude is over twice as large as expected, rejecting the canonical, exclusively kinematic interpretation of the CMB dipole with a p-value of 5 × 10−7 (4.9σ for a normal distribution, one-sided), the highest significance achieved to date in such studies. Our results are in conflict with the cosmological principle, a foundational assumption of the concordance ΛCDM model.

We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport. General discussion is illustrated by numerical analysis of a model for micron-size particle manipulated by optical tweezers.

The question of the transition to global isotropy from our anisotropic local universe is studied using the Union 2 catalogue of Type Ia supernovae (SNe Ia). We construct a ‘residual’ statistic sensitive to systematic shifts in their brightness in different directions and use this to search in different redshift slices for a preferred direction on the sky in which the SNe Ia are brighter or fainter relative to the standard Λcold dark matter (ΛCDM) cosmology. At low redshift (z < 0.05), we find that an isotropic model such as ΛCDM is barely consistent with the SNe Ia data at 2σ–3σ. A maximum‐likelihood analysis of peculiar velocities confirms this finding – there is a bulk flow of 260 km s−1 extending out to z∼ 0.06, which disagrees with ΛCDM at 1σ–2σ. Since the Shapley concentration is believed to be largely responsible for this bulk flow, we make a detailed study of the infall region: the SNe Ia falling away from the Local Group towards Shapley are indeed significantly dimmer than those falling towards us on to Shapley. Convergence to the CMB rest frame must occur well beyond Shapley (z > 0.06) so this low‐redshift bulk flow will systematically bias any reconstruction of the expansion history of the Universe. At higher redshifts z > 0.15 the agreement between the SNe Ia data and the ΛCDM model does improve, however, the sparseness and low quality of the data mean that the latter cannot be singled out as the preferred cosmological model.

We generate the peculiar velocity field for the 2MASS Redshift Survey (2MRS) catalog (Huchra et al. 2005) using an orbit-reconstruction algorithm. The reconstructed velocities of individual objects in 2MRS are well-correlated with the peculiar velocities obtained from high-precision observed distances within 3,000 km s −1 . We estimate the mean matter density to be Ω m = 0.31 ± 0.05 by comparing observed to reconstructed velocities in this volume. The reconstructed motion of the Local Group in the rest frame established by distances within 3,000 km s −1 agrees with the observed motion and is generated by fluctuations within this volume, in agreement with observations. Having tested our method against observed distances, we reconstruct the velocity field of 2MRS in successively larger radii, to study the problem of convergence towards the CMB dipole. We find that less than half of the amplitude of the CMB dipole is generated within a volume enclosing the Hydra-Centaurus-Norma supercluster at around 40h −1 Mpc. Although most of the amplitude of the CMB dipole seems to be recovered by 120h −1 Mpc, the direction does not agree and hence we observe no convergence up to this scale. Due to dominant superclusters such as Shapley or Horologium-Reticulum in the southern hemisphere at scales above 120h −1 Mpc, one might need to go well beyond 200h −1 Mpc to fully recover the dipole vector.We develop a statistical model which allows us to estimate cosmological parameters from the reconstructed growth of convergence of the velocity of the Local Group towards the CMB dipole motion. For scales up to 60h −1 Mpc, assuming a Local Group velocity of 627 km s −1 , we estimate Ω m h 2 = 0.11 ± 0.06 and σ 8 = 0.9 ± 0.4, in agreement with WMAP5 measurements at the 1-σ level. However, for scales up to 100h −1 Mpc, we obtain Ω m h 2 = 0.08 ± 0.03 and σ 8 = 1.0 ± 0.4, which agrees at the 1 to 2-σ level with WMAP5 results.

We show that the deterministic past history of the Universe can be uniquely reconstructed from the knowledge of the present mass density field, the latter being inferred from the 3D distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales -- a few Mpc -- where multi-streaming becomes significant. Above 6 Mpc/h we propose and implement an effective Monge-Ampere-Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge (1781). After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than cubic time complexity in N and reasonable CPU time requirements. Testing against N-body cosmological simulations gives over 60% of exactly reconstructed points. We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge-Ampere equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. Self-contained discussion of relevant notions and techniques is provided.Comment: 26 pages, 14 figures; accepted to MNRAS. Version 2: numerous minour clarifications in the text, additional material on the history of the Monge-Ampere equation, improved description of the auction algorithm, updated bibliography. Version 3: several misprints correcte

Observations reveal a "bulk flow" in the local Universe which is faster and extends to much larger scales than are expected around a typical observer in the standard ΛCDM cosmology. This is expected to result in a scale-dependent dipolar modulation of the acceleration of the expansion rate inferred from observations of objects within the bulk flow. From a maximum-likelihood analysis of the Joint Light-curve Analysis catalogue of Type Ia supernovae, we find that the deceleration parameter, in addition to a small monopole, indeed has a much bigger dipole component aligned with the cosmic microwave background dipole, which falls exponentially with redshift z: q 0 = q m + q d .n exp(−z/S ). The best fit to data yields q d = −8.03 and S = 0.0262 (⇒ d ∼ 100 Mpc), rejecting isotropy (q d = 0) with 3.9σ statistical significance, while q m = −0.157 and consistent with no acceleration (q m = 0) at 1.4σ. Thus the cosmic acceleration deduced from supernovae may be an artefact of our being non-Copernican observers, rather than evidence for a dominant component of "dark energy" in the Universe. Key words. cosmology: observations -dark energy -large-scale structure of UniverseArticle published by EDP Sciences L13, page 1 of 6 A&A 631, L13 (2019)

Reconstructing the density fluctuations in the early Universe that evolved into the distribution of galaxies we see today is a challenge of modern cosmology.1 An accurate reconstruction would allow us to test cosmological models by simulating the evolution starting from the reconstructed state and comparing it to the observations. Several reconstruction techniques have been proposed, 2-9 but they all suffer from lack of uniqueness because the velocities of galaxies are usually not known. Here we show that reconstruction can be reduced to a well-determined problem of optimisation, and present a specific algorithm that provides excellent agreement when tested against data from N-body simulations. By applying our algorithm to the new redshift surveys now under way, 10 we will be able to recover reliably the properties of the primeval fluctuation field of the local Universe and to determine accurately the peculiar velocities (deviations from the Hubble expansion) and the true positions of many more galaxies than is feasible by any other method.Starting from the available data on the galaxy distribution, can we trace back in time and map to its initial locations the highly structured distribution of mass in the Universe (Fig. 1)? Here we show that, with a suitable hypothesis, the knowledge of both the present non-uniform distribution of mass and of its primordial quasi-uniform distribution uniquely determines the inverse Lagrangian map, defined as the transformation from present (Eulerian) positions x to the respective initial (Lagrangian) positions q.We first consider the direct Lagrangian map q → x, which can be approximately written in terms of a potential as x = ∇ q Φ(q) at those scales where nonlinearity stays moderate.11 This is supported by numerical N-body simulations showing good agreement with a very simple potential approximation, due to Zel 'dovich, 12 which assumes that the particles move on straight trajectories. Even better agreement is obtained with a refinement, the second-order Lagrangian perturbation method, 13-16 also known to be potential. FIG. 1.N -body simulation output (present epoch) used for testing our reconstruction method. In the standard model of structure formation, the distribution of matter in the Universe is believed to have emerged from a very smooth initial state: tiny irregularities of the gravitational potential, which we can still observe as temperature fluctuations of the cosmic microwave background, gave rise to density fluctuations, which grew under their self-gravity, developing a rich and coherent pattern of structures. Most of the mass is in the form of cold dark matter; the luminous matter (galaxies) can be assumed to trace -up to some form of bias -the underlying dark matter. Shown here is a projection onto the x-y plane of a 10% slice of the simulation box of size 200h −1 Mpc. The model, ΛCDM, uses cold dark matter with cosmological constant and the following parameters: Hubble constant h = 0.65, density parameters ΩΛ = 0.7 and Ωm = 0.3, normalization factor σ8 = 0...

Previous studies have found our velocity in the rest frame of radio galaxies at high redshift to be much larger than that inferred from the dipole anisotropy of the cosmic microwave background. We construct a full sky catalogue, NVSUMSS, by merging the NVSS and SUMSS catalogues and removing local sources by various means including cross-correlating with the 2MRS catalogue. We take into account both aberration and Doppler boost to deduce our velocity from the hemispheric number count asymmetry, as well as via a 3-dimensional linear estimator. Both its magnitude and direction depend on cuts made to the catalogue, e.g. on the lowest source flux, however these effects are small. From the hemispheric number count asymmetry we obtain a velocity of 1729 ± 187 km s −1 i.e. about 4 times larger than that obtained from the CMB dipole, but close in direction, towards RA= 149 • ± 2 • , dec = −17 • ± 12 • . With the 3dimensional estimator, the derived velocity is 1355 ± 174 km s −1 towards RA= 141 • ± 11 • , dec=−9 • ±10 • . We assess the statistical significance of these results by comparison with catalogues of random distributions, finding it to be 2.81σ (99.75% confidence).