The Redshift Dependence of the Alcock–Paczynski Effect: Cosmological Constraints from the Current and Next Generation Observations.

The tomographic Alcock–Paczynski (AP) test is a robust large-scale structure (LSS) measurement that receives little contamination from the redshift space distortion. It has placed tight cosmological constraints by using small and intermediate clustering scales of the LSS data. However, previous works have neglected the cross-correlation among different redshift bins, which could cause the statistical uncertainty being underestimated by ∼20%. In this work, we further improve this method by including this multi-redshift’s full correlation. We apply it to the SDSS DR12 galaxies sample and find out that, for ΛCDM, the combination of AP with the Planck+BAO data set slightly reduces (within 1σ) Ω_m to 0.304 ± 0.007 (68.3% CL). This then leads to a larger H₀ and also mildly affects Ω_bh² and n_s as well as the derived parameters z_*, r_*, and z_re but not τ, A_s, and σ₈. For the flat wCDM model, our measurement gives Ω_m = 0.301 ± 0.010 and w = −1.090 ± 0.047, where the additional AP measurement reduces the error budget by ∼25%. When including more parameters into the analysis, the AP method also improves the constraints on Ω_k, , and N_eff by 20%–30%. Early universe parameters such as and r, however, are unaffected. Assuming the dark energy equation of state , the Planck+BAO+SNe Ia+H₀+AP data sets prefer a dynamical dark energy at ≈1.5σ CL. Finally, we forecast the cosmological constraints expected from the DESI galaxy survey and find that combining AP with the CMB+BAO method would improve the w₀–w_a constraint by a factor of ∼10. [ABSTRACT FROM AUTHOR]