  The apparent shape of galaxy clustering depends on the adopted cosmology used
to convert observed redshift to comoving distance, the $r(z)$ relation, as it
changes the line elements along and across the line of sight differently. The
Alcock-Paczy\'nski (AP) test exploits this property to constrain the expansion
history of the universe. We present an extensive review of past studies on the
AP test. We adopt an extended AP test method introduced by Park et al. (2019),
which uses the full shape of redshift-space two-point correlation function (CF)
as the standard shape, and apply it to the SDSS DR7, BOSS, and eBOSS LRG
samples covering the redshift range up to $z=0.8$.We calibrate the test against
the nonlinear cosmology-dependent systematic evolution of the CF shape using
the Multiverse simulations. We focus on examining whether or not the flat
$\Lambda$CDM `concordance' model is consistent with observation. We constrain
the flat $w$CDM model to have $w=-0.892_{-0.050}^{+0.045}$ and
$\Omega_m=0.282_{-0.023}^{+0.024}$ from our AP test alone, which is
significantly tighter than the constraints from the BAO or SNe I$a$ methods by
a factor of 3 - 6. When the AP test result is combined with the recent BAO and
SNe I$a$ results, we obtain $w=-0.903_{-0.023}^{+0.023}$ and
$\Omega_m=0.285_{-0.009}^{+0.014}$. This puts a strong tension with the flat
$\Lambda$CDM model with $w=-1$ at $4.2\sigma$ level. Consistency with $w=-1$ is
obtained only when the Planck CMB observation is combined. It remains to see if
this tension between observations of galaxy distribution at low redshifts and
CMB anisotropy at the decoupling epoch becomes greater in the future studies
and leads us to a new paradigm of cosmology.
