Constraints on small-scale cosmological fluctuations from SNe lensing dispersion

TL;DR

This paper investigates how small-scale cosmological fluctuations affect supernova lensing dispersion, using simulations to show non-linear evolution diminishes initial power spectrum enhancements, thus weakly constraining primordial parameters.

Contribution

It provides new insights into the non-linear evolution of small-scale power spectra and their impact on lensing dispersion constraints on primordial fluctuations.

Findings

Non-linear evolution reduces initial small-scale power enhancements.

Lensing dispersion weakly constrains primordial running parameters.

Including baryonic effects can tighten constraints comparable to Planck.

Abstract

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. For example, even if the linear power spectrum at $k>10h {\rm Mpc}^{-1}$ is enhanced by $1-2$ orders of magnitude, the enhancement much decreases to a factor of $2-3$ at late time ($z \leq 1.5$). Therefore, the lensing dispersion induced by the dark matter fluctuations weakly constrains the running parameters. When including baryon-cooling effects (which strongly enhance the small-scale clustering), the constraint is comparable or tighter than the PLANCK constraint, depending on the UV cut-off. Further investigations of the non-linear matter spectrum with baryonic processes is needed to reach a firm constraint.