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

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.