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.
