Model Selection using Baryon Acoustic Oscillations in the Final SDSS-IV
  Release
  The baryon acoustic oscillation (BAO) peak, seen in the cosmic matter
distribution at redshifts up to ~3.5, reflects the continued expansion of the
sonic horizon first identified in temperature anisotropies of the cosmic
microwave 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 and
the clustering of quasars. In conjunction with the Alcock-Paczy\'nski (AP)
effect, which arises from the changing ratio of angular to spatial/redshift
size of (presumed) spherically-symmetric source distributions with distance,
the BAO measurement is viewed as one of the most powerful tools to use in
assessing the geometry of the Universe. In this paper, we employ five BAO peak
measurements from the final release of the Sloan Digital Sky Survey IV, at
average redshifts <z>=0.38, 0.51, 0.70, 1.48 and 2.33, to carry out a direct
head-to-head comparison of the standard model, Lambda-CDM, and one of its
principal competitors, known as the R_h=ct universe. For completeness, we
complement the AP diagnostic with a volume-averaged distance probe that assumes
a constant comoving distance scale r_d. Both probes are free of uncertain
parameters, such as the Hubble constant, and are therefore ideally suited for
this kind of model selection. We find that R_h=ct is favored by these
measurements over the standard model based solely on the AP effect, with a
likelihood ~75% versus ~25%, while Planck-Lambda-CDM is favored over R_h=ct
based solely on the volume-averaged distance probe, with a likelihood ~80%
versus ~20%. A joint analysis using both probes produces an inconclusive
outcome, yielding comparable likelihoods to both models. We are therefore not
able to confirm with this work that the BAO data, on their own, support an
accelerating Universe.
