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The apparent shape of galaxy clustering depends on the adopted cosmology usedto convert observed redshift to comoving distance, the $r(z)$ relation, as itchanges the line elements along and across the line of sight differently. TheAlcock-Paczy\'nski (AP) test exploits this property to constrain the expansionhistory of the universe. We present an extensive review of past studies on theAP 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 LRGsamples covering the redshift range up to $z=0.8$.We calibrate the test againstthe nonlinear cosmology-dependent systematic evolution of the CF shape usingthe Multiverse simulations. We focus on examining whether or not the flat$\Lambda$CDM `concordance' model is consistent with observation. We constrainthe 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 issignificantly tighter than the constraints from the BAO or SNe I$a$ methods bya factor of 3 - 6. When the AP test result is combined with the recent BAO andSNe 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 $w=-1$ isobtained only when the Planck CMB observation is combined. It remains to see ifthis tension between observations of galaxy distribution at low redshifts andCMB anisotropy at the decoupling epoch becomes greater in the future studiesand leads us to a new paradigm of cosmology.

Tomographic Alcock-Paczynski Test with Redshift-Space Correlation Function: Evidence for the Dark Energy Equation of State Parameter w>-1