CMB Analysis With A Differentiable Likelihood

CMB Analysis With A Differentiable Likelihood#

Authors:: L. Balkenhol, C. Trendafilova, K. Benabed, S. Galli
Paper:
Source:: Lbalkenhol/candl
Documentation:

candl is a differentiable likelihood framework for analysing CMB power spectrum measurements. Key features are:

JAX-compatibility, allowing for fast and easy computation of gradients and Hessians of the likelihoods.
The latest public data releases from the South Pole Telescope and Atacama Cosmology Telescope collaborations.
Interface tools for work with other popular cosmology software packages (e.g. Cobaya and MontePython).
Auxiliary tools for common analysis tasks (e.g. generation of mock data).

candl supports the analysis of primary CMB and lensing power spectrum data (\(TT\), \(TE\), \(EE\), \(BB\), \(\phi\phi\), \(\kappa\kappa\)).

Installation#

candl can be installed with pip:

pip install candl-like

or alternatively you can clone and pip install . this repository.

Data Sets#

candl data sets are kept separately from the code. There currently exist three online libraries with compatible data:

spt_candl_data: official data repository of the South Pole Telescope collaboration.
spt_candl_forecasts: official repository of forecast likelihoods of the South Pole Telescope collaboration.
candl_data: repository of CMB data sets re-implemented in candl.
clipy: 2018 Planck likelihoods available through a wrapper with the python, JAX-friendly clipy implementation.

Together these provide access to the following data:

Data set	Library	Papers
SPT-3G D1 T&E	spt_candl_data	Camphuis et al. 2025 Quan et al. 2025 (in prep.)
SPT-3G D1 BB	spt_candl_data lite version: candl_data	Zebrowski et al. 2025
SPT-3G 2018 TT/TE/EE	candl_data	Balkenhol et al. 2023 Dutcher et al. 2021
SPT-3G 2018 \(\phi\phi\)	candl_data	Pan et al. 2023
SPT-3G Ext-10k forecast	spt_candl_forecasts	Vitrier et al. 2025
SPTpol BB	candl_data	Sayre et al. 2020
Planck 2018 likelihoods	clipy	Planck 2018 V
ACT DR6 TT/TE/EE	candl_data	Naess et al. 2025 Louis et al. 2025 Calabrese et al. 2025
ACT DR6 \(\phi\phi\)	candl_data	Madhavacheril et al. 2023 Qu et al. 2023
ACT DR4 TT/TE/EE	candl_data	Aiola et al. 2020 Choi et al. 2020

Detailed, installation instructions for the data sets can be found on the dedicated repo pages, but in short, for the spt_candl_data and the candl_data libraries you navigate to where you would like to store the data and then run:

git clone https://github.com/SouthPoleTelescope/spt_candl_data.git
cd spt_candl_data
pip install .

or:

git clone https://github.com/Lbalkenhol/candl_data.git
cd candl_data
pip install .

Instructions on how you can add your own data sets can be found in the docs.

JAX#

JAX is a Google-developed python library. In its own words: “JAX is Autograd and XLA, brought together for high-performance numerical computing.”

candl is written in a JAX-friendly way. That means JAX is optional and you can install and run candl without JAX and perform traditional inference tasks such as MCMC sampling with Cobaya. However, if JAX is installed, the likelihood is fully differentiable thanks to automatic differentiation and many functions are jitted for speed.