Abstract
We present the Einstein-Boltzmann module of the DISCO-DJ (DIfferentiable
Simulations for COsmology - Done with JAX) software package. This module
implements a fully differentiable solver for the linearised cosmological
Einstein-Boltzmann equations in the JAX framework, and allows computing
Jacobian matrices of all solver output with respect to all input parameters
using automatic differentiation. This implies that along with the solution for
a given set of parameters, the tangent hyperplane in parameter space is known
as well, which is a key ingredient for cosmological inference and forecasting
problems as well as for many other applications. We discuss our implementation
and demonstrate that our solver agrees at the per-mille level with the existing
non-differentiable solvers CAMB and CLASS, including massive neutrinos and a
dark energy fluid with parameterised equation of state. We illustrate the
dependence of various summary statistics in large-scale structure cosmology on
model parameters using the differentiable solver, and finally demonstrate how
it can be easily used for Fisher forecasting. Since the implementation is
significantly shorter and more modular than existing solvers, it is easy to
extend our solver to include additional physics, such as additional dark energy
models, modified gravity, or other non-standard physics.
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