  The Cosmic Microwave Background (CMB) radiation lensing is a promising tool
to study the physics of early universe. In this work we probe the imprints of
deviations from isotropy and scale invariance of primordial curvature
perturbation power spectrum on CMB lensing potential and convergence.
Specifically, we consider a scale-dependent hemispherical asymmetry in
primordial power spectrum. We show that the CMB lensing potential and
convergence and also the cross-correlation of the CMB lensing and late time
galaxy convergence can probe the amplitude and the scale dependence of the
dipole modulation. As another example, we consider a primordial power spectrum
with local feature. We show that the CMB lensing and the cross-correlation of
the CMB lensing and galaxy lensing can probe the amplitude and the shape of the
local feature. We show that the cross correlation of CMB lensing convergence
and galaxy lensing is capable to probe the effects of local features in power
spectrum on smaller scales than the CMB lensing. Finally we showed that the
current data can constrain the amplitude and moment dependence of dipole
asymmetry.
