Analytic auto-differentiable CDM cosmography
arXiv:2212.01937 · doi:10.1088/1475-7516/2023/07/065
Abstract
I present general analytic expressions for distance calculations (comoving distance, time coordinate, and absorption distance) in the standard CDM 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 mock type Ia supernovae using variational inference.
matches published version; 12 pages, 5 figures + appendix; phytorch available at https://github.com/kosiokarchev/phytorch
References in corpus (24)
- The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
- A Hierarchical Bayesian SED Model for Type Ia Supernovae in the Optical to Near-Infrared
- FlowPM: Distributed TensorFlow Implementation of the FastPM Cosmological N-body Solver
- Field Level Neural Network Emulator for Cosmological N-body Simulations
- GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling
- SICRET: Supernova Ia Cosmology with truncated marginal neural Ratio EsTimation
- Using wavelets to capture deviations from smoothness in galaxy-scale strong lenses
- Auto-Differentiable Spectrum Model for High-Dispersion Characterization of Exoplanets and Brown Dwarfs
- A Differentiable Model of the Assembly of Individual and Populations of Dark Matter Halos
- DSPS: Differentiable Stellar Population Synthesis
- Phase Retrieval and Design with Automatic Differentiation
- Differentiable Cosmological Simulation with Adjoint Method
- Efficient Gravitational Wave Template Bank Generation with Differentiable Waveforms
- A differentiable N-body code for transit timing and dynamical modeling. I. Algorithm and derivatives
- Numerical Strategies of Computing the Luminosity Distance
- Kernel Phase and Coronagraphy with Automatic Differentiation
- pmwd: A Differentiable Cosmological Particle-Mesh -body Library
- Differentiable Predictions for Large Scale Structure with SHAMNet
- Strong-lensing source reconstruction with variationally optimised Gaussian processes
- Analytic Light Curve for Mutual Transits of Two Bodies Across a Limb-darkened Star
- CosmicRIM : Reconstructing Early Universe by Combining Differentiable Simulations with Recurrent Inference Machines
- A new analytical solution for the distance modulus in flat cosmology
- On the Perturbative Picture and the Chang-Refsdal Lens Approximation for Planetary Microlensing
- An analytical solution in the complex plane for the luminosity distance in flat cosmology