A

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) 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-D ₂ < 1.7 × 10 ^-3 (2 σ) 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 ΛCDM fiducial cosmology with CMB-derived parameters, and measuring the quasar bias relative to this ΛCDM 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 ΛCDM model on the whole 10 < r < 1200 h ^-1 Mpc range. For the matter distribution we obtain 3-D ₂ < 5 × 10 ^-5 (2 σ) over the range 250 < r < 1200 h ^-1 Mpc, consistent with homogeneity on large scales.