Effects of neutrino mass and asymmetry on cosmological structure formation

TL;DR

This paper investigates how neutrino masses and chemical potentials influence cosmic structure formation and the matter power spectrum, using N-body simulations and MCMC-refined cosmological parameters, revealing a degeneracy between neutrino mass and degeneracy parameters.

Contribution

It provides a comprehensive evaluation of neutrino mass and chemical potential effects on the matter power spectrum with empirical formulas and introduces a new parameter to characterize their combined impact.

Findings

Neutrino mass suppresses the matter power spectrum.

Neutrino degeneracy parameters enhance the matter power spectrum.

A new combined parameter $m_\nu - \frac{4}{3}\eta^2$ effectively characterizes neutrino effects.

Abstract

Light but massive cosmological neutrinos do not cluster significantly on small scales, due to their high thermal velocities. With finite masses, cosmological neutrinos become part of the total matter field and contribute to its smoothing. Structure formation in the presence of massive neutrinos is therefore impeded compared to that in the standard $\Lambda$CDM cosmology with massless neutrinos. Neutrinos' masses also distort the anisotropy power spectrum of cosmic microwave background (CMB). Furthermore, a finite chemical potential $\mu$ for cosmological neutrinos, still allowed by current data, would have a non-negligible impact on CMB and structure formation. We consistently evaluate effects of neutrino masses and chemical potentials on the matter power spectrum by use of a neutrino-involved N-body simulation, with cosmological parameters obtained from a Markov-Chian Moonte-Carlo (MCMC) refitting of CMB data. Our results show that while a finite averaged neutrino mass $m_\nu$ tends to suppress the matter power spectrum in a range of wave numbers, the neutrino degeneracy parameters ${\xi_i \equiv \mu_i /T}$ ($i=$1, 2, 3) enhance the latter, leading to a large parameter degeneracy between $m_\nu$ and $\xi_i$. We provide an empirical formula for the effects on the matter power spectrum in a selected range of wave numbers induced by $m_\nu$ and $\eta \equiv \sqrt{\sum_i \xi^2_i}$. Observing a strong correlation between $m_\nu$ and $\eta$, we propose a single redshift-independent parameter $m_\nu - \frac{4}{3}\eta^2$ to characterize the neutrino effects on the matter power spectrum.