CMB lensing in a modified $\mathrm{\Lambda }$CDM model in light of the $H_0$ tension

The observed discrepancy of the Hubble parameter measurements in the local universe with the cosmic microwave background (CMB) data may indicate a new physics. It is vital to test the alternative models that reconcile the Hubble tension with other cosmological observations in this direction. The CMB lensing is a crucial observation that relates the early universe perturbations to the matter’s late-time distribution. In this work, we study the prediction of the "u$\mathrm{\Lambda }$CDM as a solution for $H_0$ tension for CMB lensing and the low- and high-$\mathrm{\ell }$’s temperature (TT) power spectrum internal inconsistency. We show that this model relaxes the low- and high-$\mathrm{\ell }$’s TT mild inconsistency and the CMB lensing tensions simultaneously. Accordingly, "u$\mathrm{\Lambda }$CDM having the same number of free parameters as $\mathrm{\Lambda }$CDM with lensing amplitude $A_L$ added, has a better fit with $\mathrm{\Delta }{\chi }^2=-3.3$.