Consistency test on the cosmic evolution

We propose a new and robust method to test the consistency of the cosmic evolution given by a cosmological model. It is realized by comparing the combined quantity r_d^CMB/D_V^SN , which is derived from the comoving sound horizon r_d from cosmic microwave background (CMB) measurements and the effective distance D_V derived from low-redshift type-Ia supernovae (SNe Ia) data, with direct and independent r_d/D_V obtained by baryon acoustic oscillation (BAO) measurements at median redshifts. We apply this test method for the Λ cold dark matter (Λ CDM ) and w CDM models, and investigate the consistency of the derived value of r_d/D_V from Planck 2015 and the SN Ia data sets of Union2.1 and joint light-curve analysis (JLA) (z <1.5 ), and the r_d/D_V directly given by BAO data from six-degree-field galaxy survey (6dFGS), Sloan Digital Sky Survey Data Release 7 Main Galaxy Survey (SDSS-DR7 MGS), DR11 of SDSS-III, WiggleZ and Ly α forecast surveys from baryon oscillation spectroscopic data (BOSS) DR-11 over 0.1 <z <2.36 . We find that r_d^CMB/D_V^SN for both nonflat Λ CDM and flat w CDM models with Union2.1 and JLA data are well consistent with the BAO and CMB measurements within 1 σ C.L. Future surveys will further tighten up the constraints significantly, and provide a stronger test on the consistency.