Shape of CMB lensing in the early dark energy cosmology

Recently, the cosmological tensions, $H_0$ and $S_8$ in particular, have inspired modification of both pre- and postrecombination physics simultaneously. Early dark energy is a promising pre-recombination solution of the $H_0$ tension, known to be compatible with the cosmic microwave background (CMB). However, the compatibility of early dark energy, as well as general early resolutions, with the CMB is no longer obvious if the late Universe is also modified. Aside from cosmological parameters, the main channel through which late Universe physics affects CMB observables is gravitational lensing. We employed a new method of sampling functions using the Gaussian Process in the Monte Carlo Markov Chain analysis to constrain the shape of the CMB lensing potential. We obtained the early Universe (CMB) only constraints on the full shape of the CMB lensing potential, with the late-time Universe being marginalized over. It is found that CMB data prefers a lensing potential shape that is $\Lambda$CDM-like at $80\lesssim L\lesssim400$ but with enhanced amplitude beyond this range. The obtained shape constraints can serve as a CMB-compatibility guideline for both late and early Universe model building that modifies the lensing potential.