Abstract
I present general analytic expressions for distance calculations (comoving distance, time coordinate, and absorption distance) in the standard ΛCDM cosmology, allowing for the presence of radiation and for non-zero curvature. The solutions utilise the symmetric Carlson basis of elliptic integrals, which can be evaluated with fast numerical algorithms that allow trivial parallelisation on GPUs and automatic differentiation without the need for additional special functions. I introduce a PyTorch-based implementation in the phytorch.cosmology package and briefly examine its accuracy and speed in comparison with numerical integration and other known expressions (for special cases). Finally, I demonstrate an application to high-dimensional Bayesian analysis that utilises automatic differentiation through the distance calculations to efficiently derive posteriors for cosmological parameters from up to 106 mock type Ia supernovæ using variational inference.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
