Precision calculation of $N_{\text{eff}}$ with Neutrino Direct Simulation Monte Carlo

TL;DR

This paper introduces a comprehensive neutrino Monte Carlo solver that accurately models neutrino decoupling in the early Universe, incorporating complex physical effects to refine the calculation of the effective number of neutrino species.

Contribution

The authors develop a complete $ u$DSMC solver that includes electron mass, neutrino oscillations, and QED corrections, providing high-precision $N_{ ext{eff}}$ calculations.

Findings

Calculated $N_{ ext{eff}}$ with high precision, $3.0439 \,\pm\, 0.0006$

Results agree with previous state-of-the-art calculations

Demonstrated the solver's capability for detailed cosmological neutrino modeling

Abstract

Neutrino Direct Simulation Monte Carlo ($\nu$DSMC) is a Monte Carlo method for solving the neutrino Boltzmann equation in the early Universe, designed to track the evolution of cosmic neutrinos across a wide range of cosmological scenarios. We develop a complete $\nu$DSMC solver that consistently incorporates the effects of the electron mass, three-flavour neutrino oscillations, and finite-temperature QED corrections to the thermodynamics of the electromagnetic plasma. As a first application, we perform a high-precision calculation of neutrino decoupling in the standard cosmological model and obtain $N_{\text{eff}} = 3.0439 \pm 0.0006$, in excellent agreement with state-of-the-art results.