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The standard model of cosmology with nearly Gaussian, isotropic, scaleinvariant and adiabatic initial conditions describes the cosmologicalobservations well. However, the study of any deviation from the mentionedconditions will open up a new horizon to the physics of early universe. In thiswork, we study the effect of the oscillatory and step-like features inpotentials of inflationary models in late time large scale structureobservations. Mainly we study the matter power spectrum, number density of thestructures, dark matter halo bias and specifically CMB lensing. We show thatthe oscillatory models can introduce some degeneracy with late time effects onBAO scale. We also conclude that high frequency oscillatory models which arefavored by Planck data do not have significant effect on the non linearstructure formation. Finally we show that inflationary models with stepfunctions which deviates from the standard model in small scales $l \leq 1 Mpc$can be constrained by future experiments via CMB lensing. We propose the ideathat CMB lensing is a bias independent observation which can be used as a smallscale physics probe due to distribution of the lenses in low redshifts.Meantime this model can alter the prediction of the cosmological model for thenumber density of small structures and can be used as a probable explanationfor galactic scale crisis of $\Lambda$CDM.

Late time sky as a probe of steps and oscillations in primordial Universe