Abstract 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–Paczyński (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., which uses the full shape of redshift-space two-point correlation function (CF) as the standard shape, and apply it to the Sloan Digital Sky Survey 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 Multiverse simulations. We focus on examining whether or not the flat Lambda cold dark matter (ΛCDM) concordance model is consistent with observation. We constrain the flat w CDM model to have w = − 0.892 − 0.050 + 0.045 and Ω m = 0.282 − 0.023 + 0.024 from our AP test alone, which is significantly tighter than the constraints from the BAO or SNe Ia methods by a factor of 3–6. When the AP test result is combined with the recent BAO and SNe Ia results, we obtain w = − 0.903 − 0.023 + 0.023 and Ω m = 0.285 − 0.009 + 0.014 . This puts a strong tension with the flat ΛCDM model with w = −1 at the 4.2 σ level. Consistency with w = −1 is obtained only when the Planck cosmic microwave background (CMB) observation is combined. It remains to be seen whether this tension between observations of galaxy distribution at low redshifts and CMB anisotropy at the decoupling epoch becomes greater in future studies and leads us to a new paradigm of cosmology.