[Paper Review] LINX: A Fast, Differentiable, and Extensible Big Bang Nucleosynthesis Package

Cara Giovanetti, Mariangela Lisanti+3 more|arXiv (Cornell University)|Aug 26, 2024

Genetics, Bioinformatics, and Biomedical ResearchBiochemistry, Genetics and Molecular Biology5 citations

TL;DR

LINX is a fast, differentiable BBN code built with JAX that enables gradient-based parameter inference and joint CMB+BBN analyses for standard and Delta Neff scenarios.

ABSTRACT

We introduce LINX (Light Isotope Nucleosynthesis with JAX), a new differentiable public Big Bang Nucleosynthesis (BBN) code designed for fast parameter estimation. By leveraging JAX, LINX achieves both speed and differentiability, enabling the use of Bayesian inference, including gradient-based methods. We discuss the formalism used in LINX for rapid primordial elemental abundance predictions and give examples of how LINX can be used. When combined with differentiable Cosmic Microwave Background (CMB) power spectrum emulators, LINX can be used for joint CMB and BBN analyses without requiring extensive computational resources, including on personal hardware.

Motivation & Objective

• Provide a fast, accurate, and differentiable Big Bang Nucleosynthesis (BBN) code suitable for Bayesian inference.
• Enable joint analyses of BBN with CMB data via differentiable pipelines and CMB emulators.
• Offer an extensible, user-friendly codebase that can incorporate beyond-SBBN scenarios and new physics.

Proposed method

• Implement BBN in Python using JAX for compilation, vectorization, and automatic differentiation.
• Two-stage computation: (i) compute background cosmology and thermodynamic quantities; (ii) compute primordial abundances using the background and nuclear/weak reaction rates.
• Model the neutron-proton interconversion rates via weak processes and normalize to the neutron lifetime as a nuisance parameter.
• Construct a nuclear reaction network and integrate abundance evolution with a JAX-based ODE solver (Diffrax, Tsitouras 5/4).
• Provide differentiable thermodynamic quantities through differentiable polylogarithms, gamma functions, and Bessel-function-based integrals for massive species.
• Support SBBN and SBBN+ΔNeff as default scenarios, with a modular structure enabling easy incorporation of new physics.

Experimental results

Research questions

• RQ1 How can a BBN code be made fast and differentiable to enable gradient-based inference in cosmology?
• RQ2 Can LINX perform joint, fully differentiable analyses with CMB models to constrain ΛCDM parameters and N_eff?
• RQ3 How do background thermodynamics and energy transfer between electromagnetic and neutrino sectors affect primordial abundances under standard and ΔNeff scenarios?
• RQ4 What are the advantages of LINX’s modular framework for exploring beyond-SBBN physics?

Key findings

• LINX achieves speed comparable to existing fast BBN codes while adding differentiability for gradient-based inference.
• LINX explicitly computes the energy transfer between EM and neutrino sectors, enabling consistent beyond-SBBN scenarios (e.g., ΔNeff).
• The code’s background integration yields N_eff values in agreement with state-of-the-art determinations (e.g., N_eff ≈ 3.044 for their setup).
• Differentiability enables gradient-based sampling methods and efficient joint analyses with differentiable CMB emulators (e.g., CosmoPower).
• LINX supports joint CMB+BBN analyses demonstrated in a fully differentiable pipeline with ΛCDM + N_eff, combining LINX with differentiable CMB codes.