Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A 14 $h^{-3}$ Gpc$^3$ study of cosmic homogeneity using BOSS DR12 quasar
  sample   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 redshift range
$2.2<z<2.8$ in a model-independent way, independent of any FLRW fiducial
cosmology, resulting in $3-\langle D_2 \rangle < 1.7 \times 10^{-3}$ (2
$\sigma$) over the range $250<r<1200 \, h^{-1}$Mpc for the quasar distribution.
If we assume that quasars do not have a bias much less than unity, this implies
spatial isotropy of the matter distribution on large scales. Then, combining
with the Copernican principle, we finally get homogeneity of the matter
distribution on large scales. Alternatively, using a flat $\Lambda$CDM fiducial
cosmology with CMB-derived parameters, and measuring the quasar bias relative
to this $\Lambda$CDM model, our data provide a consistency check of the model,
in terms of how homogeneous the Universe is on different scales. $D_2(r)$ is
found to be compatible with our $\Lambda$CDM model on the whole $10<r<1200 \,
h^{-1}$Mpc range. For the matter distribution we obtain $3-\langle D_2 \rangle
< 5 \times 10^{-5}$ (2 $\sigma$) over the range $250<r<1200 \, h^{-1}$Mpc,
consistent with homogeneity on large scales.

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The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
18
The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex