Is excess smoothing of Planck CMB anisotropy data partially responsible for evidence for dark energy dynamics in other w (z) CDM parametrizations?

In this paper, we study spatially-flat dynamical dark energy parametrizations, w(z)CDM, with redshift-dependent dark energy equation of state parameter w(z) expressed using three different quadratic and other polynomial forms (as functions of 1-a, where a is the scale factor), without and with a varying cosmic microwave background (CMB) lensing consistency parameter AL. We use Planck CMB anisotropy data (P18 and lensing) and a large, mutually-consistent non-CMB data compilation that includes Pantheon+ type Ia supernova, baryon acoustic oscillation (BAO), Hubble parameter (H(z)), and growth factor (fσ₈) measurements, but not recent DESI BAO data. The six w(z)CDM (+A_L) parametrizations show higher consistency between the CMB and non-CMB data constraints compared to the XCDM (+A_L) and w₀w_aCDM (+A_L) cases. Constraints from the most-restrictive P18+lensing+non-CMB data compilation on the six w(z)CDM (+A_L) parametrizations indicate that dark energy dynamics is favored over a cosmological constant by ≳2σ when A_L=1, but only by ≳1σ when A_L is allowed to vary (and A_L>1 at ∼2σ significance). Non-CMB data dominate the P18+lensing+non-CMB compilation at low z and favor quintessence-like dark energy. At high z P18+lensing data dominate, favoring phantom-like dark energy with significance from 1.5σ to 2.9σ when A_L=1, and from 1.1σ to 1.8σ when A_L varies. These results suggest that the observed excess weak lensing smoothing of some of the Planck CMB anisotropy multipoles is partially responsible for the A_L=1 cases ≳2σ evidence for dark energy dynamics over a cosmological constant.