Constraints on small-scale cosmological fluctuations from SNe lensing dispersion

Understand

We provide predictions on small-scale cosmological density power spectrum from supernova lensing dispersion.

• Parameterizing the primordial power spectrum with running $\alpha$ and running of running $\beta$ of the spectral index, we exclude large positive $\alpha$ and $\beta$ parameters which induce too large lensing dispersions over current observational upper bound.
• We ran cosmological N-body simulations of collisionless dark matter particles to investigate non-linear evolution of the primordial power spectrum with positive running parameters.
• The initial small-scale enhancement of the power spectrum is largely erased when entering into the non-linear regime.