The Most Probable Behaviour of the Dark Energy Equation of State Indicates a Thawing Quintessence Field: Tomographic Alcock-Paczy\'nski Test with Redshift-Space Correlation Function II

Abstract

We apply an extended Alcock-Paczy\'nski (AP) test to the Sloan Digital Sky Survey data to constrain the dark energy models with the Chevallier-Polarski-Linder (CPL) parametrization of the dark energy equation of state. The extended AP test method uses the full shape of redshift-space two-point correlation funcion(CF) as the standard shape in order to measure the expansion history of the universe. We calibrate the standard shape by using the cosmology-dependent nonlinear evolution of the CF shape in the Multiverse simulations. Further validation of the method and calibration of possible systematics are performed based on mock samples from the Horizon Run 4 simulation. Using the AP test alone, we constrain the flat CDM plus CPL-type dark energy model (flat $w^{\rm CPL}$CDM) to have $\Omega_m=0.290_{-0.031}^{+0.029}$, $w_0=-0.800_{-0.100}^{+0.208}$, and $w_a=-0.238_{-0.972}^{+0.650}$. When combined with other results from the low-redshift universe, such as the Pantheon$+$ supernova compilation and DESI BAO data, the constraint on dark energy becomes $w_0=-0.857_{-0.042}^{+0.051}$, and $w_a=-0.153_{-0.356}^{+0.347}$. The best-fit $w^{CPL}(z)$ suggests no phantom-divide crossing at $z<0.7$, and the dark energy behaviour is consistent with a thawing quintessence field. It is only when the CMB data are combined with late-time cosmological probes that a phantom-divide crossing at low redshift is favored.