5 pages, 2 figures, Talk presented at The 51th Rencontres de Moriond, March 19-26, 2016, La Thuile, Italy; to appear in the Moriond Conference Proceedings
In this study, we probe the cosmic homogeneity with the BOSS CMASS galaxy sample in the redshift region of $0.43 < z < 0.7$. We use the normalised counts-in-spheres estimator $\mathcal{N}(<r)$ and the fractal correlation dimension $\mathcal{D}_{2}(r)$ to assess the homogeneity scale of the universe. We verify that the universe becomes homogenous on scales greater than $\mathcal{R}_{H} \simeq 64.3\pm1.6\ h^{-1}Mpc$, consolidating the Cosmological Principle with a consistency test of $Λ$CDM model at the percentage level. Finally, we explore the evolution of the homogeneity scale in redshift.
In this paper, we study the characteristic scale of transition to cosmic homogeneity of the universe, $\mathcal{R}_H$, as a standard ruler, to constrain cosmological parameters on mock galaxy catalogues. We use mock galaxy catalogues that simulate the CMASS galaxy sample of the BOSS survey in the redshift range $0.43 \leq z \leq 0.7$. In each redshift bin we obtain the homogeneity scale, defined as the scale at which the universe becomes homogeneous to $1\%$, i.e. $D_2(\mathcal{R}_H) = 2.97$. With a simple Fisher analysis, we find that the performance of measuring the cosmological parameters w…
In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, $3\ h^{-3}\ \mathrm{Gpc}^3$ at $0.43 \leq z \leq 0.7$. We study the scaled counts-in-spheres, $\mathcal{N}(<r)$, and the fractal correlation dimension, $\mathcal{D}_2(r)$, to assess the homogeneity scale of the universe using a $Landy\ \&\ Szalay$ inspired estimator. Defining the scale of transition to homogeneity as the scale at which $\mathcal{D}_2(r)$ reaches 3 within $1\%…
The combination of Galaxy-Galaxy Lensing (GGL) and Redshift Space Distortion of galaxy clustering (RSD) is a privileged technique to test General Relativity predictions, and break degeneracies between the growth rate of structure parameter $f$ and the amplitude of the linear power-spectrum $σ_8$. We perform a joint GGL and RSD analysis on 250 sq. degrees using shape catalogues from CFHTLenS and CFHT-Stripe 82, and spectroscopic redshifts from the BOSS CMASS sample. We adjust a model that includes non-linear biasing, RSD and Alcock-Paczynski effects. We find $f(z=0.57) =0.95\pm0.23$, $σ_8(z=0.5…
We probe the angular scale of homogeneity in the local Universe using blue galaxies from the SDSS survey as a cosmological tracer. Through the scaled counts in spherical caps, $ \mathcal{N}(<θ) $, and the fractal correlation dimension, $\mathcal{D}_{2}(θ)$, we find an angular scale of transition to homogeneity for this sample of $θ_{\text{H}} = 22.19^{\circ} \pm 1.02^{\circ}$. A comparison of this measurement with another obtained using a different cosmic tracer at a similar redshift range ($z < 0.06$), namely, the HI extragalactic sources from the ALFALFA catalogue, confirms that both results…
We present the first measurement of the homogeneity index, $\mathcal{H}$, a fractal or Hausdorff dimension of the early Universe from the Planck CMB temperature variations $δT$ in the sky. This characterization of the isotropy scale is model-free and purely geometrical, independent of the amplitude of $δT$. We find evidence of homogeneity ($\mathcal{H}=0$) for scales larger than $θ_{\mathcal{H}} = 65.9 \pm 9.2 °$ on the CMB sky. This finding is at odds with the $Λ$CDM prediction, which assumes a scale invariant infinite universe. Such anomaly is consistent with the well known low quadrupule am…
The most massive and luminous galaxies in the Universe serve as powerful probes to study the formation of structure, the assembly of mass, and cosmology. However, their detailed formation and evolution is still barely understood. Here we extract a sample of massive mock galaxies from the semi-analytical model of galaxy formation (SAM) GALACTICUS from the MultiDark-Galaxies, by replicating the CMASS photometric selection from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). The comparison of the GALACTICUS CMASS-mock with BOSS-CMASS data allows us to explore different aspects of the…
We use the scaled counts in spherical caps $\mathcal{N}(<θ)$ and the fractal correlation dimension $ \mathcal{D}_{2}(θ) $ procedures to search for a transition scale to homogeneity in the local universe as given by the ALFALFA catalogue (a sample of extragalactic HI line sources, in the redshift range $0 < z < 0.06$). Our analyses, in the 2-dimensional sky projected data, show a transition to homogeneity at $θ_H = 16.49^{\circ} \pm 0.29^{\circ}$, in remarkable accordance with the angular scale expected from simulations, a result that strengthens the validity of the cosmological principle in th…
Cosmology relies on the Cosmological Principle, i.e., the hypothesis that the Universe is homogeneous and isotropic on large scales. This implies in particular that the counts of galaxies should approach a homogeneous scaling with volume at sufficiently large scales. Testing homogeneity is crucial to obtain a correct interpretation of the physical assumptions underlying the current cosmic acceleration and structure formation of the Universe. In this Letter, we use the Baryon Oscillation Spectroscopic Survey to make the first spectroscopic and model-independent measurements of the angular homog…
A Large Quasar Group (LQG) of particularly large size and high membership has been identified in the DR7QSO catalogue of the Sloan Digital Sky Survey. It has characteristic size (volume^1/3) ~ 500 Mpc (proper size, present epoch), longest dimension ~ 1240 Mpc, membership of 73 quasars, and mean redshift <z> = 1.27. In terms of both size and membership it is the most extreme LQG found in the DR7QSO catalogue for the redshift range 1.0 <= z <= 1.8 of our current investigation. Its location on the sky is ~ 8.8 deg north (~ 615 Mpc projected) of the Clowes & Campusano LQG at the same redshift, <z>…
A 2.29 GHz VLBI all-sky survey of ultra-compact radio sources has formed the basis of a number of cosmological investigations, which examine the relationship between angular-size and redshift. Here I use a sample of 468 such sources with 0.5<z<=3.787, to investigate the isotropy of the Universe. The sample is divided into hemispherical sub-samples, over an all-sky 5 degree x 5 degree array, each of which is allowed to determine a value of Omega_m, assuming that we are living in a spatially flat homogeneous isotropic LambdaCDM model. If we regard the latter as a null hypothesis, then it fails t…
In the era of precision cosmology, we investigate an novel method to probe the Dark Universe. By studying the fractality of the universe, we estimate a characteristic scale of homogeneity. Using a fisher analysis, we investigate the potential impact of this scale to the cosmological information we can gain from the Euclid satellite, and therefore understand the nature of Dark Energy and Dark matter of our universe.
In this paper, we study the homogeneity of the GRB distribution using a subsample of the Greiner GRB catalogue, which contains 314 objects with redshift $0<z<2.5$ (244 of them discovered by the Swift GRB Mission). We try to reconcile the dilemma between the new observations and the current theory of structure formation and growth. To test the results against the possible biases in redshift determination and the incompleteness of the Greiner sample, we also apply our analysis to the 244 GRBs discovered by Swift and the subsample presented by the Swift Gamma-Ray Burst Host Galaxy Legacy Survey (…
Homogeneity scale in the local Universe: Model-independent estimate from S-PLUS iDR6 blue galaxies
Observatório Nacional（国家天文台）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）；Observatório do Valongo（瓦隆戈天文台）；The Observatories of the Carnegie Institution for Science（卡内基科学机构天文台）；Rubin Observatory Project Office（鲁宾天文台项目办公室）；Departamento de Física, Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学物理系）；Universidade de São Paulo, IAG（圣保罗大学天文学、地球科学与气象学学院）
How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedman-Lemaitre-Robertson-Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables …
We propose a method to probe the homogeneity of a general universe, without assuming symmetry. We show that isotropy can be tested at remote locations on the past lightcone by comparing the line-of-sight and transverse expansion rates, using the time dependence of the polarization of Cosmic Microwave Background photons that have been inverse-Compton scattered by the hot gas in massive clusters of galaxies. This probes a combination of remote transverse and parallel components of the expansion rate of the metric, and we may use radial baryon acoustic oscillations or cosmic clocks to measure the…
The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret observations of the CMB and the galaxy distribution. However, homogeneity cannot be directly observed in the galaxy distribution or CMB, even with perfect observations, since we observe on the past lightcone and not on spatial surfaces. We can directly observe and test for isotropy, but to link this to homogeneity, we need to assume the Copern…
Assuming the universe is spatially homogeneous on the largest scales lays the foundation for almost all cosmology. This idea is based on the Copernican principle, that we are not at a particularly special place in the universe. Surprisingly, this philosophical assumption has yet to be rigorously demonstrated independently of the standard paradigm. This issue has been brought to light by cosmological models which can potentially explain apparent acceleration by spatial inhomogeneity rather than dark energy. These models replace the temporal fine tuning associated with Lambda with a spatial fine…
As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test this hypothesis we calculate the general analytical formula to fifth order for the redshift spherical shell mass. Using the same analytical method we write the metric in the light-cone by introducing a gauge invariant quantity $G(z)$ which together with the luminosity distance $D_L(z)$ completely determine the light-cone geometry of a LTB model.
Using the 2MASS Photometric Redshift catalogue we perform a number of statistical tests aimed at detecting possible departures from statistical homogeneity and isotropy in the large-scale structure of the Universe. Making use of the angular homogeneity index, an observable proposed in a previous publication, as well as studying the scaling of the angular clustering and number counts with magnitude limit, we place constraints on the fractal nature of the galaxy distribution. We find that the statistical properties of our sample are in excellent agreement with the standard cosmological model, an…
The Universe on comoving scales larger than 100 Mpc/h is assumed to be statistically homogeneous, with the transition scale where we have $1\%$ deviation from homogeneity being known as the homogeneity scale $R_H$. The latter was recently proposed in Ntelis et al. (2018) [arXiv:1810.09362] to be a standard ruler. In this paper we perform a comparison between the baryon acoustic oscillations and the homogeneity scales $R_H$, assuming a spatially flat universe, linear cosmological perturbation theory and the cosmological constant cold dark matter $Λ$CDM model. By direct theoretical calculations,…
General relativistic effects have long been predicted to subtly influence the observed large-scale structure of the universe. The current generation of galaxy redshift surveys have reached a size where detection of such effects is becoming feasible. In this paper, we report the first detection of the redshift asymmetry from the cross-correlation function of two galaxy populations which is consistent with relativistic effects. The dataset is taken from the Sloan Digital Sky Survey DR12 CMASS galaxy sample, and we detect the asymmetry at the $2.7σ$ level by applying a shell-averaged estimator to…
New observations of high-redshift objects are crucial for the improvement of the standard $Λ$CDM cosmological model and our understanding of the Universe. One of the main directions of modern observational cosmology is the analysis of the large-scale structure of Universe, in particular, in deep fields. We study the large-scale structure of the Universe along the line of sight using the latest version of the COSMOS2015 catalogue, which contains 518,404 high quality photometric redshifts of galaxies selected in the optical range of the COSMOS field ($2\times 2$ deg$^2$), with depth up to the re…
It is generally assumed that on sufficiently large scales the Universe is well-described as a homogeneous, isotropic FRW cosmology with a dark energy. Does the formation of nonlinear cosmic inhomogeneities produce a significant effect on the average large-scale FLRW dynamics? As an answer, we suggest that if the length scale at which homogeneity sets in is much smaller than the Hubble length scale, the back-reaction due to averaging over inhomogeneities is negligible. This result is supported by more than one approach to study of averaging in cosmology. Even if no single approach is sufficient…
In this paper, we study the normalised characteristic scale of transition to cosmic homogeneity, $\mathcal{R}_H/d_V$, as a cosmological probe. We use a compilation of SDSS galaxy samples, comprising more than $10^6$ galaxies in the redshift range $0.17 \leq z \leq 2.2$ within the largest comoving volume to date, $\sim 8 h^{-3}\mathrm{Gpc}^3$. We show that these samples can be described by a single bias model as a function of redshift. By combining our measurements with prior Cosmic Microwave Background and Lensing information from the Planck satellite, we constrain the total matter density rat…
Fluctuations in sky maps of the galaxy redshifts, dubbed as angular redshift fluctuations (ARF), contain precise information about the growth rate of structures and the nature of gravity in the Universe. Specifically, ARF constrain the combination of cosmological parameters $H/H_0\,fσ_8(z)$, while being an intrinsically tomographic probe and largely insensitive to many observational systematic errors, all this without requiring the assumption of any redshift-to-distance relation under a given fiducial cosmology. We present the first cosmological constraints derived from ARF by using BOSS LOWZ+…
We carry out multifractal analyses of multiple tracers namely the main galaxy sample, the LRG sample and the quasar sample from the SDSS to test the assumption of cosmic homogeneity and identify the scale of transition to homogeneity, if any. We consider the behaviour of the scaled number counts and the scaling relations of different moments of the galaxy number counts in spheres of varying radius $R$ to calculate the spectrum of the Minkowski-Bouligand general dimension $D_{q} (R)$ for $-4 \leq q \leq 4$. The present analysis provides us the opportunity to study the spectrum of the generalize…
We suggest a new explanation for the observed large scale flatness, homogeneity and isotropy of the universe. The basic ingredients are elementary and well-known, namely Einstein's theory of gravity and Hawking's method of computing gravitational entropy. The new twist is provided by the boundary conditions we recently proposed for "big bang" type singularities dominated by conformal matter, enforcing $CPT$ symmetry and analyticity. Here, we show that, besides allowing us to describe the big bang, these boundary conditions allow new gravitational instantons, enabling us to calculate the gravit…
A plethora of observational data obtained over the last couple of decades has allowed cosmology to enter into a precision era and has led to the foundation of the standard cosmological constant and cold dark matter paradigm, known as the $Λ$CDM model. Given the many possible extensions of this concordance model, we present here several novel consistency tests which could be used to probe for deviations from $Λ$CDM. First, we derive a joint consistency test for the spatial curvature $Ω_{k,0}$ and the matter density $Ω_\textrm{m,0}$ parameters, constructed using only the Hubble rate $H(z)$, whic…
A correspondence between the Equivalence principle and the homogeneity of the universe is discussed. In Newtonian gravity, translation of co-moving coordinates in a uniformly expanding universe defines an accelerated frame. A consistency condition for the invariance of this transformation which requires a well defined transformation for the Newtonian potential, yields the Friedmann equations. All these symmetries are lost when we modify NSL (Newton's Second Law) or the Poisson equation. For example by replacing NSL with non-linear function of the acceleration the concept of relative accelerati…
We propose a novel approach to obtain the growth rate of cosmic structures, $f(z)$, from the evolution of the cosmic homogeneity scale, $R_{\text{H}}(z)$. Our methodology needs two ingredients in a specific functional form: $R_{\text{H}}(z)$ data and the matter two-point correlation function today, i.e., $ξ(r, z=0)$. We use a Gaussian Process approach to reconstruct the function $R_{\text{H}}$. In the absence of suitable observational information of the matter correlation function in the local Universe, $z \simeq 0$, we assume a fiducial cosmology to obtain $ξ(r, z=0)$. For this reason, our fi…
We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as possible the questions of gaussianity, homogeneity and isotropy from each other. We focus both on isotropic estimators of non-gaussianity as well as statistically anisotropic estimators of gaussianity, giving particular emphasis on their signatures and the enhanced "cosmic variances" that become increasingly important as our putative Universe becomes less symmetr…
The BOSS quasar sample is used to study cosmic homogeneity with a 3D survey in the redshift range $2.2<z<2.8$. We measure the count-in-sphere, $N(<\! r)$, i.e. the average number of objects around a given object, and its logarithmic derivative, the fractal correlation dimension, $D_2(r)$. For a homogeneous distribution $N(<\! r) \propto r^3$ and $D_2(r)=3$. Due to the uncertainty on tracer density evolution, 3D surveys can only probe homogeneity up to a redshift dependence, i.e. they probe so-called "spatial isotropy". Our data demonstrate spatial isotropy of the quasar distribution in the red…
We use 12 large quasar group (LQG) samples to investigate the homogeneity of $0.5\lesssim z \lesssim 2$ Universe ($z$ denotes the redshift). We calculate the bias factor $b$ and the two-point correlation function $ξ_{\rm LQG}$ for such groups for three different density profiles of the LQG dark matter halos, i.e. the isothermal profile, the Navarro-Frenk-White (NFW) profile, and the (gravitational) lensing profile. We consider the $Λ$CDM concordance model of our Universe with $Ω_m=0.28$, $Ω_Λ=0.72$, the Hubble constant $H_0=100h~$km s$^{-1}$ Mpc$^{-1}$ with $h=0.72$ in our calculations. Dividi…
Measurements of the Angular Homogeneity Scale from DESI DR1
Observatório Nacional（国家天文台）；Universidade Federal Rural do Rio de Janeiro（里约热内卢联邦农村大学）；Zhejiang University（浙江大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）
There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around $t\rightarrow 0$, where $t$ is the physical time. One is related to the past geodesic completeness of the inflationary trajectory due to the presence of a cosmological singularity, and the other one is related to the homogeneity condition required to inflate a local space-time patch of the universe. We will show that both the problems have a common origin, arising from how the causal structure of null and timelike geodesics are structur…
A Universe with finite age also has a finite causal scale $χ_§$, so the metric can not be homogeneous for $χ>χ_§$, as it is usually assumed. To account for this, we propose a new causal boundary condition, that can be fulfil by fixing the cosmological constant $Λ$ (a free parameter for gravity). The resulting Universe is inhomogeneous, with possible variation of cosmological parameters on scales $χ\simeq χ_§$. The size of $χ_§$ depends on the details of inflation, but regardless of its size, the boundary condition forces $Λ/8πG $ to cancel the contribution of a constant vacuum energy $ρ_{vac}$…
It is argued that cosmic chronometers yield estimates of the spatially averaged expansion rate even in a universe that is not well described by a global FLRW model - as long as the Universe is statistically homogeneous and isotropic with a sufficiently small homogeneity scale. On the other hand, measurements of the expansion rate based on observations of redshift drift will not in general yield estimates of the spatially averaged expansion rate - but it will in the case where the universe is described well by a single FLRW model on large scales. Therefore, a disagreement between measurements o…
The apparent accelerating expansion of the Universe is forcing us to examine the foundational aspects of the standard model of cosmology -- in particular, the fact that dark energy is a direct consequence of the homogeneity assumption. We discuss the foundations of the assumption of spatial homogeneity, in the case when the Copernican Principle is adopted. We present results that show how (almost-) homogeneity follows from (almost-) isotropy of various observables. The analysis requires the fully nonlinear field equations -- i.e., it is not possible to use second- or higher-order perturbation …
We perform large-scale cosmological simulations that solve Einstein's equations directly via numerical relativity. Starting with initial conditions sampled from the cosmic microwave background, we track the emergence of a cosmic web without the need for a background cosmology. We measure the backreaction of large-scale structure on the evolution of averaged quantities in a matter-dominated universe. Although our results are preliminary, we find the global backreaction energy density is of order $10^{-8}$ compared to the energy density of matter in our simulations, and is thus unlikely to expla…
The concordance of the $Λ$CDM cosmological model in light of current observations has been the subject of an intense debate in recent months. The 2018 Planck Cosmic Microwave Background (CMB) temperature anisotropy power spectrum measurements appear at face value to favour a spatially closed Universe with curvature parameter $Ω_K<0$. This preference disappears if Baryon Acoustic Oscillation (BAO) measurements are combined with Planck data to break the geometrical degeneracy, although the reliability of this combination has been questioned due to the strong tension present between the two datas…
The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greatest structures in the universe. This point is closely related to whether or not such a distribution can be approximated as being homogeneous on large enough scales. Here we assess this problem by considering the size distribution of superclusters of galaxies and by leveraging on the properties of Zipf-Mandelbrot law, providing a novel approach which complements stand…
One of the possible extensions of Einstein's General Theory of Relativity consists in allowing for the presence of spacetime torsion. The form of the underlying torsion tensor can be chosen such that the homogeneity and isotropy of Friedmann-Lemaitre-Robertson-Walker universes is preserved, and it has been recently suggested that such universes may undergo accelerating phases. We use recent low-redshift data, coming from Type Ia Supernova and Hubble parameter measurements, to phenomenologically constrain this class of models under the so-called steady-state torsion assumption of a constant fra…
