Dark energy and lensing anomaly in Planck CMB data

In this paper, we investigate the impact of the lensing anomaly in Planck cosmic microwave background (CMB) data on the nature of dark energy (DE). We constrain the state equation ($w_0,w_a$) of DE with the lensing scaling parameter $A_L=1$ and varying $A_L$, using the Planck PR3 and two updated Planck PR4 likelihoods, CamSpec and HiLLiPoP respectively, combined with DESI baryon acoustic oscillation (BAO) and Pantheon+ supernova data. As expected, when $A_L$ is allowed to vary, the evolving DE is not preferred due to the degeneracy between $w_0,w_a$ and $A_L$. In particular, we also consider replacing DESI BAO data with pre-DESI BAO in our analysis, and observe that DESI BAO appears to exacerbate the lensing anomaly, which is caused by the smaller matter density $\Omega_m$ it prefers, however, this effect can be offset by the shifts in $w_0$ and $w_a$ preferring the evolving DE. Our work indicates that the lensing anomaly in Planck data is worth carefully reconsidering when new cosmological survey data is combined with CMB.