Lensing dispersion of SNIa and small scales of the primordial power spectrum

Probing the primordial power spectrum at small scales is crucial for discerning inflationary models, especially if BICEP2 results are confirmed. We demonstrate this necessity by briefly reviewing single small field models that give a detectable gravitational waves signal, thus being degenerate with large field models on CMB scales. A distinct prediction of these small field models is an enhancement of the power spectrum at small scales, lifting up the degeneracy. We propose a way to detect this enhancement, and more generally, different features in the power spectrum at small scales $1\lesssim k \lesssim 10^2-10^3 \,\mathrm{Mpc}^{-1}$ by considering the existing data of lensing dispersion in Type Ia supernovae. We show that for various deviations from the simplest $n_s\simeq 0.96$ the lensing dispersion cuts considerably into the allowed parameter space by PLANCK and constrains the spectrum to smaller scales beyond the reach of other current data sets.