Consistency of the nonflat $\Lambda$CDM model with the new result from BOSS

Abstract

Using 137,562 quasars in the redshift range $2.1\leq z\leq3.5$ from the Data Release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of Sloan Digital Sky Survey (SDSS)-III, the BOSS-SDSS collaboration estimated the expansion rate $H(z=2.34)=222\pm7$ km/s/Mpc of Universe, and reported that this value is in tension with the predictions of flat $\Lambda$CDM model at around 2.5$\sigma$ level. In this paper, we briefly describe some attempts made in the literature to relieve the tension, and show that the tension can naturally be alleviated in non-flat $\Lambda$CDM model with positive curvature. We also perform the observational consistency check by considering the constraints on the non-flat $\Lambda$CDM model from Planck,WP and BAO data. We find that the non-flat $\Lambda$CDM model constrained with Planck+WP data fits better to the line of sight measurement $H(z=2.34)=222\pm7$ km/s/Mpc, but only at the expense of still having a poor fit to the BAO transverse measurements.