A joint 2-and 3-point clustering analysis of the VIPERS PDR2 catalogue at z ∼ 1: breaking the degeneracy of cosmological parameters

We measure the galaxy two- and three-point correlation functions at z = [0.5, 0.7] and z = [0.7, 0.9], from the Public Data Release 2 (PDR2) of the VIMOS Public Extragalactic Redshift Survey (VIPERS). We model the two statistics including a non-linear one-loop model for the two-point function and a tree-level model for the three-point function, and perform a joint likelihood analysis. The entire process and non-linear corrections are tested and validated through the use of the 153 highly realistic VIPERS mock catalogues, showing that they are robust down to scales as small as 10 h(-1) Mpc. The mocks are also adopted to compute the covariance matrix that we use for the joint two- and three-point analysis. Despite the limited statistics of the two (volume-limited) subsamples analysed, we demonstrate that such a combination successfully breaks the degeneracy existing at two-point level between clustering amplitude sigma(8), linear bias b(1), and the linear growth rate of fluctuations f. For the latter, in particular, we measure f (z = 0.61) = 0.64(-0.37)(+0.55) and f(z = 0.8) = 1.0 +/- 1.0, while the amplitude of clustering is found to be sigma(8) (z = 0.61) = 0.50 +/- 0.12 and sigma(8)(z = 0.8) = 0.39(-0.13)(+0.11). These values are in excellent agreement with the extrapolation of a Planck cosmology.

Automated summary

In this study, the galaxy two- and three-point correlation functions at specific redshifts were measured and analyzed using a joint likelihood analysis approach. Through the use of highly realistic VIPERS mock catalogs, the process and non-linear corrections were validated, demonstrating robustness down to small scales. The combination of two statistics successfully breaks the degeneracy between clustering amplitude, linear bias, and linear growth rate, providing measurements in excellent agreement with a Planck cosmology.