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Register a new userMeasuring the cosmic homogeneity scale with SDSS-IV DR16 Quasars
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Rodrigo De Sousa Goncalves
Publication date
2020
fields
Physics
and research's language is
English
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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.
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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.
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 $70 h^{-1} {rm Mpc}$.
We show that a large-area imaging survey using narrow-band filters could detect quasars in sufficiently high number densities, and with more than sufficient accuracy in their photometric redshifts, to turn them into suitable tracers of large-scale structure. If a narrow-band optical survey can detect objects as faint as i=23, it could reach volumetric number densities as high as 10^{-4} h^3 Mpc^{-3} (comoving) at z~1.5 . Such a catalog would lead to precision measurements of the power spectrum up to z~3-4. We also show that it is possible to employ quasars to measure baryon acoustic oscillations at high redshifts, where the uncertainties from redshift distortions and nonlinearities are much smaller than at z<1. As a concrete example we study the future impact of J-PAS, which is a narrow-band imaging survey in the optical over 1/5 of the unobscured sky with 42 filters of ~100 A full-width at half-maximum. We show that J-PAS will be able to take advantage of the broad emission lines of quasars to deliver excellent photometric redshifts, sigma_{z}~0.002(1+z), for millions of objects.
We have made the largest-volume measurement to date of the transition to large-scale homogeneity in the distribution of galaxies. We use the WiggleZ survey, a spectroscopic survey of over 200,000 blue galaxies in a cosmic volume of ~1 (Gpc/h)^3. A new method of defining the homogeneity scale is presented, which is more robust than methods previously used in the literature, and which can be easily compared between different surveys. Due to the large cosmic depth of WiggleZ (up to z=1) we are able to make the first measurement of the transition to homogeneity over a range of cosmic epochs. The mean number of galaxies N(<r) in spheres of comoving radius r is proportional to r^3 within 1%, or equivalently the fractal dimension of the sample is within 1% of D_2=3, at radii larger than 71 pm 8 Mpc/h at z~0.2, 70 pm 5 Mpc/h at z~0.4, 81 pm 5 Mpc/h at z~0.6, and 75 pm 4 Mpc/h at z~0.8. We demonstrate the robustness of our results against selection function effects, using a LCDM N-body simulation and a suite of inhomogeneous fractal distributions. The results are in excellent agreement with both the LCDM N-body simulation and an analytical LCDM prediction. We can exclude a fractal distribution with fractal dimension below D_2=2.97 on scales from ~80 Mpc/h up to the largest scales probed by our measurement, ~300 Mpc/h, at 99.99% confidence.
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