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

Abstract: 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 $A_L$. 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 ($f\sigma_8$) 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 $w_0 w_a$CDM ($+A_L$) 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 $\gtrsim 2\sigma$ when $A_L = 1$, but only by $\gtrsim 1\sigma$ when $A_L$ is allowed to vary (and $A_L>1$ at $\sim2\sigma$ 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 $1.5\sigma$ to $2.9 \sigma$ when $A_L = 1$, and from $1.1\sigma$ to $1.8\sigma$ when $A_L$ varies. These results suggest that the observed excess weak lensing smoothing of some of the Planck CMB anistropy multipoles is partially responsible for the $A_L = 1$ cases $\gtrsim 2\sigma$ evidence for dark energy dynamics over a cosmological constant.