CMB lensing from early-formed dark matter halos

Some theoretical models for the early Universe predict a spike-type enhancement in the primordial power spectrum on a small scale, which would result in forming early-formed dark matter halos~(EFHs). Some recent studies have claimed to have placed limits on such small scales, which, however, involve uncertainties, such as the physics of substructures and the halo-galaxy relations. In this work, we study the cosmic microwave background~(CMB) lensing effect, considering the existence of EFHs, and investigate the potential to probe the EFHs and the primordial perturbations on scales smaller than $1\mathrm{Mpc}$, complementing these previous studies. We numerically calculate the angular power spectrum of the lensing potential and the lensed CMB anisotropy of temperature, E-mode, and B-mode polarization, including the nonlinear effects of EFHs. We find the possibility that the lensed CMB temperature anisotropy is significantly enhanced on small scales, $\ell>1000$, and could be tested by component decomposition of observed signals through multifrequency observations. Through the calculation with different models of the spiky-type power spectrum, we demonstrate that the accurate measurements of the CMB lensing effect would provide insight into the abundance of EFHs within the limited mass range around $10^{11}~M_\odot$ and the primordial power spectrum on the limited scales around $k\sim 1\mathrm{Mpc}^{-1}$. In particular, we find that the existence of such EFHs can amplify the lensed anisotropy of CMB B-mode polarization even on large scales, $\ell <100$, as the overall enhancement by $\sim 5 \%$ level compared to the standard structure formation model without EFHs. Therefore, future CMB measurements, such as the LiteBIRD satellite, can probe the existence of the EFHs and the spike-type primordial power spectrum through the precise measurement of the large-scale CMB B-mode polarization.