Speaker
Description
The dynamics of particles in the early universe are described by Boltzmann equations, which involve high-dimensional phase space integrals. Classical approaches use quadrature integration and evolve the system on a fixed momentum grid, which scales poorly to high-dimensional integrals and parameter scans, severely limiting the complexity of processes that can be studied. We introduce Neural Boltzmann Equations (NBE), which use three coupled concepts to overcome these limitations. First, particle properties are encoded in physics-inspired neural distribution functions, with parameters that can be predicted using neural networks, enabling efficient parameter scans. Second, phase space integrals are evaluated with Monte Carlo methods, using established importance sampling tools from collider physics that benefit from the efficiency of neural distribution functions. Third, we use the natural gradient method to train the networks and evolve the system. After demonstrating the individual benefits of NBEs, we use our framework to perform a precision calculation of the number of effective neutrino degrees in the early universe.