Speaker
Description
We present a new approach to the numerical evaluation of the effects of non-cold relics on the evolution of cosmological perturbations. The Boltzmann hierarchies used to compute the contributions of these relics to the stress-energy tensor are replaced with a set of integral equations. These integral equations take the form of convolutions and are solved iteratively coupled with Einstein's equations. We develop efficient algorithms for evaluating these convolutions using non-uniform fast Fourier transforms (NUFFTs). This approach enables efficient and accurate evaluation of the cosmic microwave background anisotropies and matter power spectra, all the way through the history of the Universe, without relying on semi-analytic approximations at late times. We implement this method in the Boltzmann solver CLASS, and apply it to massive neutrino perturbations as a demonstration. Our results match the accuracy of the full Boltzmann solution while avoiding numerical artifacts from truncation of Boltzmann hierarchy at finite multipole and offering substantial speedups depending on the required precision and the range of scales of interest. This new framework provides a practical and robust alternative for the truncated Boltzmann hierarchy approach, especially for studying beyond
