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Register a new userThe scale of homogeneity of the galaxy distribution in SDSS DR6
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The assumption that the Universe, on sufficiently large scales, is homogeneous and isotropic is crucial to our current understanding of cosmology. In this paper we test if the observed galaxy distribution is actually homogeneous on large scales. We have carried out a multifractal analysis of the galaxy distribution in a volume limited subsample from the SDSS DR6. This considers the scaling properties of different moments of galaxy number counts in spheres of varying radius $r$ centered on galaxies. This analysis gives the spectrum of generalized dimension $D_q(r)$, where $q >0$ quantifies the scaling properties in overdense regions and $q<0$ in underdense regions. We expect $D_q(r)=3$ for a homogeneous, random point distribution. In our analysis we have determined $D_q(r)$ in the range $-4 le q le 4$ and $7 le r le 98 h^{-1} {rm Mpc}$. In addition to the SDSS data we have analysed several random samples which are homogeneous by construction. Simulated galaxy samples generated from dark matter N-body simulations and the Millennium Run were also analysed. The SDSS data is considered to be homogeneous if the measured $D_q$ is consistent with that of the random samples. We find that the galaxy distribution becomes homogeneous at a length-scale between 60 and $70 h^{-1} {rm Mpc}$. The galaxy distribution, we find, is homogeneous at length-scales greater than $70 h^{-1} {rm Mpc}$. This is consistent with earlier works which find the transition to homogeneity at around $70 h^{-1} {rm Mpc}$.
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We analyze a set of volume limited sample of galaxies from the SDSS to study the issue of cosmic homogeneity. We use the Renyi entropy of different order to probe the inhomogeneties present in the galaxy distributions. We also calculate the Renyi diveregence to quantify the deviations of the galaxy distribution from a homogeneous Poisson distribution on different length scales. We separately carry out the analysis using the overlapping spheres and the independent voxels. Our analysis suggests that the scale of homogeneity is underestimated in the smaller galaxy samples due to the suppression of inhomogeneities by the overlapping of the measuring speheres. We find that an analysis with the independent voxels and/or use of a significantly larger galaxy sample can help to circumvent or mitigate this problem. Combining the results from these analyses, we find that the galaxy distribution in the SDSS becomes homogeneous on a length scale beyond $140 , h^{-1}, {rm Mpc}$.
The quasar sample of the fourteenth data release of the Sloan Digital Sky Survey (SDSS-IV DR14) is used to determine the cosmic homogeneity scale in the redshift range $0.80<z<2.24$. We divide the sample into 4 redshift bins, each one with $N_{rm q} geq 19,000$ quasars, spanning the whole redshift coverage of the survey and use two correlation function estimators to measure the scaled counts-in-spheres and its logarithmic derivative, i.e., the fractal correlation dimension, $D_2$. Using the $Lambda$CDM cosmology as the fiducial model, we first estimate the redshift evolution of quasar bias and then the homogeneity scale of the underlying matter distribution $r_{rm{hom}}^{rm{m}}$. We find that $r_{rm{hom}}^{rm{m}}$ exhibits a decreasing trend with redshift and that the values obtained are in good agreement with the $Lambda$CDM prediction over the entire redshift interval studied. We, therefore, conclude that the large-scale homogeneity assumption is consistent with the largest spatial distribution of quasars currently available
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}(<theta) $, and the fractal correlation dimension, $mathcal{D}_{2}(theta)$, we find an angular scale of transition to homogeneity for this sample of $theta_{text{H}} = 22.19^{circ} pm 1.02^{circ}$. 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 are in excellent agreement (taking into account the corresponding bias correction). We also perform tests to asses the robustness of our results. For instance, we test if the size of the surveyed area is large enough to identify the transition scale we search for, and also we investigate a reduced sample of blue galaxies, obtaining in both cases a similar angular scale for the transition to homogeneity. Our results, besides confirming the existence of an angular scale of transition to homogeneity in different cosmic tracers present in the local Universe, show that the observed angular scale $theta_{text{H}}$ agrees well with what is expected in the $Lambda$CDM scenario. Although we can not prove spatial homogeneity within the approach followed, our results provide one more evidence of it, strengthening the validity of the Cosmological Principle.
We report measurements of the scale of cosmic homogeneity ($r_{h}$) using the recently released quasar sample of the sixteenth data release of the Sloan Digital Sky Survey (SDSS-IV DR16). We perform our analysis in 2 redshift bins lying in the redshift interval $2.2 < z < 3.2$ by means of the fractal dimension $D_2$. By adopting the usual assumption that $r_{h}$ is obtained when $D_2 sim 2.97$, that is, within 1% of $D_2=3$, we find the cosmic homogeneity scale with a decreasing trend with redshift, and in good agreement with the $Lambda$CDM prediction. Our results confirm the presence of a homogeneity scale in the spatial distribution of quasars as predicted by the fundamental assumptions of the standard cosmological model.
Detecting the large-scale structure of the Universe based on the galaxy distribution and characterising its components is of fundamental importance in astrophysics but is also a difficult task to achieve. Wide-area spectroscopic redshift surveys are required to accurately measure galaxy positions in space that also need to cover large areas of the sky. It is also difficult to create algorithms that can extract cosmic web structures (e.g. filaments). Moreover, these detections will be affected by systematic uncertainties that stem from the characteristics of the survey used (e.g. its completeness and coverage) and from the unique properties of the specific method adopted to detect the cosmic web (i.e. the assumptions it relies on and the free parameters it may employ). For these reasons, the creation of new catalogues of cosmic web features on wide sky areas is important, as this allows users to have at their disposal a well-understood sample of structures whose systematic uncertainties have been thoroughly investigated. In this paper we present the filament catalogues created using the discrete persistent structure extractor (DisPerSE) tool in the Sloan Digital Sky Survey (SDSS), and we fully characterise them in terms of their dependence on the choice of parameters pertaining to the algorithm, and with respect to several systematic issues that may arise in the skeleton as a result of the properties of the galaxy distribution (such as Finger-of-God redshift distortions and defects of the density field that are due to the boundaries of the survey).
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