Speaker
Description
The standard approach for computing perturbations of non-cold relics in Boltzmann solvers relies on a truncated multipole hierarchy, which introduces numerical artifacts and becomes computationally expensive at small scales. We present an alternative framework based on integral equations (IEs), where the formal solution to the collisionless Boltzmann equation is expressed as a convolution of gravitational source terms with analytic kernels. These convolutions are evaluated iteratively alongside the rest of the perturbation system using non-uniform fast Fourier transforms (NUFFTs). This method is free from truncation artifacts and is applicable to arbitrary non-cold relic species without model-specific fluid approximations. We implement this framework in CLASSIER (CLASS Integral Equation Revision), a publicly available modification of the Boltzmann solver CLASS. As a primary demonstration, we apply the IE method to massive neutrinos, achieving sub-0.1% accuracy in the matter power spectrum up to k$ \sim 100 \mathrm{Mpc}^{-1}$ with significant speedup over the conventional truncated hierarchy. We further demonstrate the generality of this framework by applying it to decaying dark matter, illustrating that the method extends naturally to non-standard non-cold relics.