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The baryon acoustic oscillation (BAO) peak, seen in the cosmic matterdistribution at redshifts up to ~3.5, reflects the continued expansion of thesonic horizon first identified in temperature anisotropies of the cosmicmicrowave background. The BAO peak position can now be measured to better than~1% accuracy using galaxies, and ~1.4-1.6% precision with Ly-alpha forrests andthe clustering of quasars. In conjunction with the Alcock-Paczy\'nski (AP)effect, which arises from the changing ratio of angular to spatial/redshiftsize of (presumed) spherically-symmetric source distributions with distance,the BAO measurement is viewed as one of the most powerful tools to use inassessing the geometry of the Universe. In this paper, we employ five BAO peakmeasurements from the final release of the Sloan Digital Sky Survey IV, ataverage redshifts <z>=0.38, 0.51, 0.70, 1.48 and 2.33, to carry out a directhead-to-head comparison of the standard model, Lambda-CDM, and one of itsprincipal competitors, known as the R_h=ct universe. For completeness, wecomplement the AP diagnostic with a volume-averaged distance probe that assumesa constant comoving distance scale r_d. Both probes are free of uncertainparameters, such as the Hubble constant, and are therefore ideally suited forthis kind of model selection. We find that R_h=ct is favored by thesemeasurements over the standard model based solely on the AP effect, with alikelihood ~75% versus ~25%, while Planck-Lambda-CDM is favored over R_h=ctbased solely on the volume-averaged distance probe, with a likelihood ~80%versus ~20%. A joint analysis using both probes produces an inconclusiveoutcome, yielding comparable likelihoods to both models. We are therefore notable to confirm with this work that the BAO data, on their own, support anaccelerating Universe.

Model Selection using Baryon Acoustic Oscillations in the Final SDSS-IV Release