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arxiv: 2606.28175 · v1 · pith:4KBBLOGRnew · submitted 2026-06-26 · 🌌 astro-ph.CO · gr-qc· hep-ph

HIcosmo: a differentiable JAX-based framework for cosmology inference

Jing-Zhao Qi , Jing-Fei Zhang , Xin Zhang This is my paper

Pith reviewed 2026-06-29 02:38 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords JAXcosmology inferenceautomatic differentiationbackground cosmologydark energy modelssupernovae likelihoodsBAOFisher forecasts
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The pith

HIcosmo builds all cosmology models and likelihoods from JAX primitives to obtain exact gradients via automatic differentiation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces HIcosmo as an open-source framework that implements forward models, distance integrals, likelihoods, sampling, and Fisher forecasts using only JAX operations for background cosmology. This construction supplies gradients and Hessians of the log-likelihood directly through automatic differentiation rather than finite differences. The framework covers LambdaCDM, wCDM, w0waCDM, and interacting dark-energy models along with likelihoods from supernovae, BAO, Planck priors, local H0, and strong-lensing time delays. Validation shows chi-squared agreement to 10^{-6} to 10^{-2} and parameter constraints within 0.2 sigma of reference codes, while end-to-end sampling reaches 8.7 times the throughput of Cobaya on CPU and up to 20 times on GPU.

Core claim

HIcosmo is a JAX-based framework in which the forward model, distance integrals, likelihood evaluations, posterior sampling, and Fisher forecasts are all built from JAX primitives. Gradients and Hessians of the log-likelihood are therefore obtained directly by automatic differentiation. The implementation covers four dark-energy models and multiple background likelihoods for supernovae, BAO, Planck distance priors, local H0, and strong-lensing time delays. It achieves 8.7 times the end-to-end sampling throughput of Cobaya on CPU with GPU acceleration up to 20 times, while chi-squared values agree to absolute differences of 10^{-6} to 10^{-2} and marginalized constraints differ by less than 0

What carries the argument

JAX primitives for the forward model and likelihood that enable automatic differentiation of the log-likelihood.

If this is right

  • Multi-probe joint constraints from supernovae, BAO, Planck, and local H0 can be computed with the reported speed gains.
  • Dark-energy equation-of-state constraints follow directly from the implemented models.
  • Fisher forecasts are generated for six 21 cm intensity-mapping surveys including SKA1, MeerKAT, BINGO, Tianlai, and CHIME.
  • The code maintains numerical agreement with reference implementations to the stated precision levels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same JAX structure could interface with external Boltzmann solvers to extend the framework beyond background cosmology.
  • GPU scaling suggests the code can handle the full volume of Stage IV survey data without additional approximations.
  • Exact gradients may support more advanced sampling algorithms that rely on first- and second-order information.

Load-bearing premise

Background-only cosmology likelihoods without full perturbation theory suffice for the validation cases and intended applications.

What would settle it

A side-by-side run of the same multi-probe analysis in HIcosmo and Cobaya that produces marginalized constraints differing by more than 0.2 sigma or chi-squared values differing by more than 0.01.

read the original abstract

The Stage IV cosmological surveys, such as Euclid, LSST, DESI, and SKA, will deliver observational data of unprecedented volume, calling for efficient and reliable inference tools. This paper presents HIcosmo (High-performance Inference for Cosmology), an open-source JAX-based framework for cosmology inference. In HIcosmo, the forward model, distance integrals, likelihood evaluations, posterior sampling, and Fisher forecasts are all built from JAX primitives, so that gradients and Hessians of the log-likelihood are obtained directly by automatic differentiation, without any finite-difference approximation. The framework implements the $\Lambda$CDM, $w$CDM, $w_0 w_a$CDM, and interacting dark-energy models, and provides likelihoods for Type Ia supernovae (Pantheon+, DES-SN5YR, Union3), baryon acoustic oscillations (DESI DR1/DR2, SDSS), Planck 2018 distance priors, local $H_0$ measurements, and strong-lensing time delays. Its scope is restricted to background cosmology, with Boltzmann solvers and full perturbation-level likelihoods left to external tools. We validate HIcosmo against the reference implementation of each likelihood and against Cobaya. $\chi^2$ values agree to absolute differences of $10^{-6}$-$10^{-2}$, and the marginalized constraints from the two codes differ by less than $0.2\sigma$ in every analysis tested. Leveraging just-in-time compilation and automatic differentiation, HIcosmo achieves about $8.7\times$ the end-to-end sampling throughput of Cobaya on CPU. As the dataset grows to survey scale, GPU acceleration over CPU reaches up to $20\times$. As applications, we present multi-probe $\Lambda$CDM joint constraints, dark-energy equation-of-state constraints, and Fisher forecasts for six 21 cm intensity-mapping surveys, including SKA1, MeerKAT, BINGO, Tianlai, and CHIME.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper introduces HIcosmo, an open-source JAX-based framework for background cosmology inference. It implements ΛCDM, wCDM, w0waCDM and interacting dark-energy models together with likelihoods for Pantheon+, DES-SN5YR, Union3, DESI/SDSS BAO, Planck 2018 distance priors, local H0 and strong-lensing time delays. All distance integrals, likelihood evaluations and sampling are expressed with JAX primitives so that gradients and Hessians are obtained by automatic differentiation. Validation against reference implementations and Cobaya shows χ² agreement to 10^{-6}–10^{-2} and marginalized constraints differing by <0.2σ; end-to-end sampling throughput is reported as 8.7× that of Cobaya on CPU and up to 20× on GPU. Applications include multi-probe joint constraints and Fisher forecasts for six 21 cm intensity-mapping surveys.

Significance. If the reported numerical agreement and speed-ups hold, the framework supplies a practical, differentiable tool for background-only cosmology analyses that will be useful for Stage-IV survey pipelines. Explicit restriction of scope to background quantities, direct validation against established codes, open-source release, and provision of Fisher forecasts for intensity-mapping experiments are concrete strengths that increase the work’s utility.

minor comments (3)
  1. [Abstract, §1] Abstract and §1: the statement that ‘gradients and Hessians … are obtained directly by automatic differentiation, without any finite-difference approximation’ would be strengthened by a brief note on how JAX handles the numerical integration of the comoving distance (e.g., which quadrature rule is used and whether it is differentiable).
  2. [Validation] Validation section: while χ² differences of 10^{-6}–10^{-2} are quoted, the text does not tabulate which likelihoods achieve the larger residuals; adding a short table or per-likelihood breakdown would make the agreement claim easier to assess.
  3. [Results] Performance paragraph: the 8.7× CPU and 20× GPU speed-up figures are given without stating the precise hardware, number of live points/chains, or burn-in settings used for the Cobaya comparison; these details belong in the methods or results section.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of HIcosmo's scope and performance, and recommendation for minor revision. The recognition of its utility for background cosmology analyses and Stage-IV pipelines is appreciated.

Circularity Check

0 steps flagged

No significant circularity; software framework with empirical validation only

full rationale

The paper describes a JAX-based software implementation of standard background cosmology models (ΛCDM, wCDM, etc.) and likelihoods (Pantheon+, DESI, Planck priors, etc.), with all operations built from JAX primitives for autodiff. Validation consists of direct numerical comparison to external reference codes and Cobaya, reporting χ² agreement and posterior shifts as empirical outcomes. No derivation chain, first-principles predictions, or fitted inputs presented as predictions exist; scope is explicitly limited to background integrals without perturbation theory. No self-citation load-bearing steps, ansatzes, or uniqueness claims appear. The performance numbers (8.7× CPU, up to 20× GPU) are tied directly to the JAX implementation and measured against external baselines, satisfying the self-contained criterion.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is a software framework release rather than a derivation; it relies on standard cosmological models and external likelihood definitions without introducing new free parameters, axioms, or entities.

axioms (1)
  • domain assumption Standard background cosmological models (ΛCDM, wCDM, w0waCDM, interacting dark energy) are correctly implemented in the code.
    The framework implements these models as its core forward models.

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discussion (0)

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Reference graph

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