Pith. sign in

REVIEW 3 major objections 4 minor 154 references

Cosmo_learn is a Python package that generates mock versions of five late-universe probes and validates them by recovering the input wCDM cosmology.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

An open-source toolkit that simulates late-universe cosmological observations and benchmarks MCMC, genetic algorithms, Gaussian processes, Bayesian ridge regression, and neural networks in one pipeline.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A clean, useful software package for generating wCDM mocks and running several inference methods, but the 'benchmarking' label outruns the evidence: the method comparisons rest on one realization and the default noise model is too simple to support the 'realistic noise' claim. the 3 major comments →

arxiv 2508.20971 v2 pith:7LXMOWDX submitted 2025-08-28 astro-ph.CO

Cosmo-Learn: code for learning cosmology using different methods and mock data

Reginald Christian Bernardo , Daniela Grand\'on , Jackson Levi Said , V\'ictor H. C\'ardenas , Gene Carlo Belinario , Reinabelle Reyes This is my paper
classification astro-ph.CO
keywords cosmological inferencemock data generationwCDMMarkov chain Monte Carlogenetic algorithmsGaussian process regressionneural networksstandard sirens
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

Cosmo_learn is an open-source Python package that builds mock versions of five late-universe datasets—cosmic chronometers, type Ia supernovae, baryon acoustic oscillations, redshift-space distortions, and gravitational-wave bright sirens—starting from a user-chosen 'true' cosmology. The paper argues that the generated mock data are statistically consistent with that input cosmology: over 100 simulated realizations, Markov-chain Monte Carlo parameter inference recovers the fiducial wCDM parameters, with stacked posteriors centered on the true values. The same pipeline then benchmarks five inference strategies—MCMC, genetic algorithms, Gaussian processes, Bayesian ridge regression, and neural networks—under identical noise assumptions. The motivating frame is the growing difficulty of comparing cosmological models amid observational tensions, so a standardized, transparent mock-data and inference environment would give the community a common test bed.

Core claim

The central claim is that cosmo_learn provides a standardized and flexible framework for benchmarking cosmological inference methods, and that the mock data it generates are internally consistent with the input cosmology. Consistency is established by construction and by validation: each mock point inherits an observed redshift, draws its value from a normal distribution centered on the true wCDM prediction with variance fixed by the real error bar, and the resulting residuals are white across realizations. MCMC over 100 realizations recovers the injected H0, Ωm0, w, S8, and rD, with stacked posteriors centered on the true values, including sub-1σ recovery of the sound horizon. The paper doe

What carries the argument

The carrying mechanism is the mock-data recipe: fix redshifts to the observed sample, draw a Gaussian mean around the true cosmology with variance set by each observed error bar, and keep the observed error bar as the mock error. This turns a real catalog into an ensemble of synthetic catalogs with known underlying parameters. Around this core, analytic wCDM background and linear perturbation solutions supply the theory predictions, and a built-in likelihood enables parameter recovery via MCMC and GA-Fisher. The validation loop—generate, infer, compare to input—is what carries the paper's central consistency claim.

Load-bearing premise

The default mock generator assumes that the real observed error bars are the correct noise amplitudes, that Gaussian noise is sufficient, and that data points are uncorrelated; for bright sirens it additionally assumes forecast mission sensitivities. If those noise assumptions do not match a real survey, benchmark conclusions drawn on the mocks may not transfer.

What would settle it

Take a benchmark question the package is meant to answer: run MCMC on mock catalogs generated with a realistic full covariance matrix or a non-Gaussian error model and compare the recovered posterior coverage. If the fraction of experiments in which the true parameters fall within the 68% credible interval departs from ~68%, the claim that the mocks are statistically consistent with the input cosmology fails for that noise model. A simpler check: the residuals of the mock data should behave as standard normal draws, so a chi-square test of residuals aggregated over realizations would expose no

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the validation claim is correct, any inference method run inside cosmo_learn can be tested directly against a known truth, making reported biases or successes interpretable without appeal to external datasets.
  • The five built-in probes span the late-universe expansion and growth history out to high redshift, so the package can serve as a common benchmark for comparing models and methods under identical noise assumptions.
  • Because the wCDM step uses analytic background and perturbation solutions, generation and likelihood evaluation are fast enough for 100-realization ensemble tests in teaching or research settings.
  • The mock-generation function is deliberately exposed and modifiable, so the same framework can accommodate full covariance matrices, different redshift draws, and additional probes without changing the inference interface.

Where Pith is reading between the lines

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

  • A natural next test, left implicit by the paper, is to run the same 100-realization recovery with a full covariance matrix between data points; if parameter recovery stays centered on truth, the default no-covariance assumption is benign, if not, the benchmarks would need their own error bars.
  • The bright-siren noise model relies on forecast mission sensitivity curves rather than actual detections, so the package's gravitational-wave benchmarks are best read as forecasts for future missions rather than statements about current data.
  • The same mock-generation core could be extended to measure reconstruction bias directly: comparing Gaussian-process or neural-network reconstructions to the true input functions per realization would quantify how each non-parametric method trades smoothness for accuracy.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper presents cosmo_learn, an open-source Python package for generating mock cosmological data for five late-universe probes (cosmic chronometers, SNe Ia, BAO, RSD, and GW bright sirens) under a fiducial wCDM cosmology, and for performing inference with MCMC, genetic algorithm plus Fisher forecast, Gaussian processes, Bayesian ridge regression, and neural networks. The authors validate the mock generation by showing white residuals over 100 realizations and by recovering the input wCDM parameters with MCMC. The package is modular, extensible, and accompanied by a public GitHub repository with tutorials. The central claim is that cosmo_learn provides a standardized framework for benchmarking cosmological inference methods with realistic noise modeling.

Significance. If the claims are fully supported, cosmo_learn would be a useful community tool for cosmology education and for controlled comparisons of inference methods. The paper's strengths include open-source code, a clear explanation of the mock-generation recipe, and a sensible internal-consistency check: the 100-realization MCMC recovery is a clean way to show that the generated data are statistically consistent with the input cosmology. The reconstruction modules (GP, BRR, ANN) are also demonstrated on concrete mock data. However, the validity of the broader benchmarking and 'realistic noise modeling' claims depends on whether the default noise treatment and the single-realization reconstruction demonstrations are sufficient; in the current form these aspects are not quantitatively established.

major comments (3)
  1. [§2.1, §3] The default mock generation draws y1 = N(y_true, (Δy_obs)^2) and assigns the same diagonal Δy_obs as the final uncertainty. The MCMC validation in §3 uses the same independent-Gaussian likelihood. This is a closed loop: it verifies internal self-consistency, not that the mocks reproduce the error structure of real observations. For Pantheon+ a published systematic covariance exists, DESI DR1 BAO bins are correlated, and RSD compilations include non-Gaussian uncertainties. The text notes that users can supply a full covariance, but all default figures and the 100-realization validation use independent errors. This undercuts the abstract's 'realistic noise modeling' claim and should be either demonstrated with covariance/non-Gaussian tests or explicitly softened.
  2. [§4.3–§4.5, Figs. 7 and 10] The GP, BRR, and ANN reconstructions are shown for a single realization only, with no quantitative recovery metrics such as bias, root-mean-square error, or credible-interval coverage over an ensemble of mocks. Visual inspection of one realization is insufficient to support the claim that cosmo_learn provides a framework for benchmarking inference methods. I recommend adding a quantitative comparison over many realizations, e.g., reporting the mean and scatter of the reconstructed functions versus the true input, and coverage probabilities of the 1σ/2σ bands.
  3. [§3, Fig. 3] The MCMC validation says parameters are recovered 'within ~1–2σ' and that stacked posteriors are Gaussian, but no quantitative coverage statistics are provided. For a validation claim, the paper should report, for the 100 realizations, the fraction of runs where the true parameter lies inside the 68% and 95% credible intervals. This would turn a qualitative statement into a falsifiable test of consistency.
minor comments (4)
  1. [§4.2] There is a syntax typo: `my_cl.ga_params['parents_portion'=0.3` is missing the closing bracket; should be `['parents_portion']=0.3`.
  2. [§2.2] Eqs. (2.10)–(2.12) use forecast eLISA sensitivity and simulated lensing/peculiar-velocity errors; the paper should note more explicitly that the GW mock is forward-modeled from forecasts, not current detections, so results using it are forecast-oriented.
  3. [References] Several references are duplicated (e.g., Planck 2018 appears as [23] and [90]; emcee as [75] and [108]). This should be cleaned up.
  4. [§4.1] The description that MCMC 'draws random samples from a normal distribution' is imprecise; the sampler draws from the proposal distribution, not from a normal in general. The text would benefit from a more careful wording.

Circularity Check

0 steps flagged

No significant circularity: the recovery test is an intentional self-consistency check, not an independent derivation.

full rationale

The paper's central validation is not a derivation of new physics but an internal calibration of mock data. Section 2.1 constructs mock measurements as y1 = N(ytrue, (dely_obs)^2), and Section 3 fits the same wCDM model with the same diagonal Gaussian likelihood to recover ytrue. This is a deliberate closed loop, explicitly described as showing that the mock data are 'statistically consistent with the input cosmology.' The paper does not present this recovery as an external prediction; it says the white residuals are 'as expected since they were drawn from a Gaussian distribution.' The load-bearing contribution of the paper is the open-source, modular software framework for generating mocks and comparing inference methods, not a cosmological claim that depends on this self-consistency test. Self-citations to the authors' earlier GA, GP, and ANN papers are background references and are not used to forbid alternatives or to justify the validity of the central framework. The abstract's phrase 'realistic noise modeling' may overstate what the default independent-Gaussian mock generator validates, especially for datasets with known covariances, but that is an accuracy/scope concern rather than circularity. No specific reduction of a claimed result to its own inputs was found, so the circularity score is 0.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The central validation rests on standard wCDM expressions from the literature and on stated mock noise assumptions. The package itself adds no new physical postulates or fitted constants beyond method hyperparameters; the main assumptions are the Gaussian, error-bar-sized noise model and forecast-based GW noise models.

free parameters (3)
  • GP kernel hyperparameters (amplitude and length scale) per probe = not reported
    Trained on mock data via marginal likelihood maximization (Eq. 4.8); part of the reconstruction methods, not the central validation claim.
  • BRR polynomial degree = 3
    Hand-chosen default for the Bayesian ridge regression reconstruction (Section 4.4).
  • ANN hidden layer size = 4096
    Hand-chosen default ReFANN architecture (Section 4.5).
axioms (5)
  • standard math wCDM background equations (Eq. 2.16) and analytical growth expressions from Nesseris and Sapone (2015)
    Used to generate mock data and compute observables; accepted from literature.
  • domain assumption Gaussian noise model for mock data (Section 2.1)
    Assumes observed error bars are the correct noise variance and that noise is Gaussian and independent; this is the core realism assumption.
  • domain assumption GW lensing, peculiar velocity, and LISA error models (Eqs. 2.10 to 2.12)
    Based on eLISA forecasts from cited works, not on actual detections.
  • domain assumption Redshift distribution of GW events from eLISA configuration L6A2M5N2 (Figure 2)
    Assumed event distribution for simulated bright siren catalogs.
  • domain assumption Spatial flatness and constant dark energy equation of state (wCDM)
    The fiducial model used throughout; a standard phenomenological choice.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Cosmo-Learn: code for learning cosmology using different methods and mock data." pith.science (2026). https://pith.science/paper/7LXMOWDX

@misc{pith2026250820971,
  author       = {Pith},
  title        = {Pith review of: Cosmo-Learn: code for learning cosmology using different methods and mock data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7LXMOWDX}},
  note         = {Machine review of arXiv:2508.20971}
}
Share X Bluesky LinkedIn Reddit HN
abstract

We present cosmo_learn, an open-source python-based software package designed to simulate cosmological data and perform data-driven inference using a range of modern statistical and machine learning techniques. Motivated by the growing complexity of cosmological models and the emergence of observational tensions, cosmo_learn provides a standardized and flexible framework for benchmarking cosmological inference methods. The package supports realistic noise modeling for key observables in the late Universe, including cosmic chronometers, supernovae Ia, baryon acoustic oscillations, redshift space distortions, and gravitational wave bright sirens. We demonstrate the internal consistency of the simulated data with the input cosmology via residuals and parameter recovery using a fiducial $w$CDM model. Built-in learning and inference modules include traditional Markov Chain Monte Carlo, as well as more recent approaches such as genetic algorithms, Gaussian processes, Bayesian ridge regression, and artificial neural networks. These methods are implemented in a modular and extensible architecture designed to facilitate comparisons across inference strategies in a common pipeline. By providing a flexible and transparent simulation and learning environment, cosmo_learn supports both educational and research efforts at the intersection of cosmology, statistics, and machine learning.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

154 extracted references · 23 canonical work pages · 22 internal anchors

  1. [1]

    Supernov a Search Team collaboration, Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201]

    Pith/arXiv arXiv 1998

  2. [2]

    Supernov a Cosmology Project collaboration, Measurements of Ω and Λ from 42 High Redshift Supernovae, Astrophys. J. 517 (1999) 565 [astro-ph/9812133]

    Pith/arXiv arXiv 1999

  3. [3]

    Di Valentino, O

    E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri et al.,In the Realm of the Hubble tension− a Review of Solutions, 2103.01183

    Pith/arXiv arXiv

  4. [4]

    Baudis,Dark matter detection, J

    L. Baudis,Dark matter detection, J. Phys. G43 (2016) 044001

    2016

  5. [5]

    Bertone, D

    G. Bertone, D. Hooper and J. Silk,Particle dark matter: Evidence, candidates and constraints, Phys. Rept. 405 (2005) 279 [hep-ph/0404175]

    Pith/arXiv arXiv 2005

  6. [6]

    Gaitskell,Direct detection of dark matter, Ann

    R. Gaitskell,Direct detection of dark matter, Ann. Rev. Nucl. Part. Sci.54 (2004) 315

    2004

  7. [7]

    P. J. E. Peebles and B. Ratra,The Cosmological constant and dark energy, Rev. Mod. Phys. 75 (2003) 559 [astro-ph/0207347]

    Pith/arXiv arXiv 2003

  8. [8]

    E. J. Copeland, M. Sami and S. Tsujikawa,Dynamics of dark energy, Int. J. Mod. Phys.D15 (2006) 1753 [hep-th/0603057]

    Pith/arXiv arXiv 2006

  9. [9]

    Baumann, D

    D. Baumann, D. Green and R. A. Porto,B-modes and the Nature of Inflation, JCAP 01 (2015) 016 [1407.2621]

    Pith/arXiv arXiv 2015

  10. [10]

    LiteBIRD collaboration, Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey, PTEP 2023 (2023) 042F01 [2202.02773]. – 25 –

    Pith/arXiv arXiv 2023

  11. [12]

    Di Valentino et al.,Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension, Astropart

    E. Di Valentino et al.,Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension, Astropart. Phys.131 (2021) 102605 [2008.11284]

    Pith/arXiv arXiv 2021

  12. [13]

    Di Valentino et al.,Cosmology intertwined III:f σ8 and S8, Astropart

    E. Di Valentino et al.,Cosmology intertwined III:f σ8 and S8, Astropart. Phys.131 (2021) 102604 [2008.11285]

    Pith/arXiv arXiv 2021

  13. [14]

    Benisty,Quantifying the S8 tension with the Redshift Space Distortion data set, Phys

    D. Benisty,Quantifying the S8 tension with the Redshift Space Distortion data set, Phys. Dark Univ. 31 (2021) 100766 [2005.03751]

    Pith/arXiv arXiv 2021

  14. [15]

    Poulin, J

    V. Poulin, J. L. Bernal, E. D. Kovetz and M. Kamionkowski,Sigma-8 tension is a drag, Phys. Rev. D 107 (2023) 123538 [2209.06217]

    Pith/arXiv arXiv 2023

  15. [16]

    Levi Said, J

    J. Levi Said, J. Mifsud, J. Sultana and K. Z. Adami,Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data, JCAP 06 (2021) 015 [2103.05021]

    Pith/arXiv arXiv 2021

  16. [17]

    Dark Univ

    CosmoVerse Network collaboration, The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics, Phys. Dark Univ. 49 (2025) 101965 [2504.01669]

    Pith/arXiv arXiv 2025

  17. [18]

    E. Abdalla et al.,Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies, JHEAp 34 (2022) 49 [2203.06142]

    Pith/arXiv arXiv 2022

  18. [19]

    A. G. Riess et al.,A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team, Astrophys. J. Lett.934 (2022) L7 [2112.04510]

    Pith/arXiv arXiv 2022

  19. [20]

    K. C. Wong et al.,H0LiCOW – XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3σ tension between early- and late-Universe probes, Mon. Not. Roy. Astron. Soc.498 (2020) 1420 [1907.04869]

    Pith/arXiv arXiv 2020

  20. [21]

    R. I. Anderson, N. W. Koblischke and L. Eyer,Small-amplitude Red Giants Elucidate the Nature of the Tip of the Red Giant Branch as a Standard Candle, Astrophys. J. Lett.963 (2024) L43 [2303.04790]

    Pith/arXiv arXiv 2024

  21. [22]

    W. L. Freedman, B. F. Madore, T. Hoyt, I. S. Jang, R. Beaton, M. G. Lee et al.,Calibration of the Tip of the Red Giant Branch (TRGB), Astrophysical Journal 891 (2020)

    2020

  22. [24]

    DES collaboration, Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing, 2105.13549

    Pith/arXiv arXiv

  23. [25]

    eBOSS collaboration, Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory, Phys. Rev. D103 (2021) 083533 [2007.08991]

    Pith/arXiv arXiv 2021

  24. [26]

    Zhang, G

    P. Zhang, G. D’Amico, L. Senatore, C. Zhao and Y. Cai,BOSS Correlation Function analysis from the Effective Field Theory of Large-Scale Structure, JCAP 02 (2022) 036 [2110.07539]

    Pith/arXiv arXiv 2022

  25. [27]

    R. J. Cooke, M. Pettini and C. C. Steidel,One Percent Determination of the Primordial Deuterium Abundance, Astrophys. J. 855 (2018) 102 [1710.11129]

    Pith/arXiv arXiv 2018

  26. [28]

    Poulin, T

    V. Poulin, T. L. Smith and T. Karwal,The Ups and Downs of Early Dark Energy solutions to the Hubble tension: A review of models, hints and constraints circa 2023, Phys. Dark Univ.42 (2023) 101348 [2302.09032]

    Pith/arXiv arXiv 2023

  27. [29]

    Di Valentino and A

    E. Di Valentino and A. Melchiorri,Neutrino Mass Bounds in the Era of Tension Cosmology, Astrophys. J. Lett.931 (2022) L18 [2112.02993]. – 26 –

    Pith/arXiv arXiv 2022

  28. [30]

    Addazi et al.,Quantum gravity phenomenology at the dawn of the multi-messenger era—A review, Prog

    A. Addazi et al.,Quantum gravity phenomenology at the dawn of the multi-messenger era—A review, Prog. Part. Nucl. Phys.125 (2022) 103948 [2111.05659]

    Pith/arXiv arXiv 2022

  29. [31]

    Akrami et al.,Modified Gravity and Cosmology

    CANTATAcollaboration, Y. Akrami et al.,Modified Gravity and Cosmology. An Update by the CANTATA Network. Springer, 2021, 10.1007/978-3-030-83715-0, [2105.12582]

    Pith/arXiv arXiv 2021

  30. [32]

    Bahamonde, K

    S. Bahamonde, K. F. Dialektopoulos, C. Escamilla-Rivera, G. Farrugia, V. Gakis, M. Hendry et al.,Teleparallel Gravity: From Theory to Cosmology, 2106.13793

    Pith/arXiv arXiv

  31. [33]

    Bamba, S

    K. Bamba, S. Capozziello, S. Nojiri and S. D. Odintsov,Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests, Astrophys. Space Sci. 342 (2012) 155 [1205.3421]

    Pith/arXiv arXiv 2012

  32. [34]

    Nojiri and S

    S. Nojiri and S. D. Odintsov,Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rept. 505 (2011) 59 [1011.0544]

    Pith/arXiv arXiv 2011

  33. [35]

    Nojiri, S

    S. Nojiri, S. Odintsov and V. Oikonomou,Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution, Phys. Rept. 692 (2017) 1 [1705.11098]

    Pith/arXiv arXiv 2017

  34. [36]

    Shafieloo and C

    A. Shafieloo and C. Clarkson,Model independent tests of the standard cosmological model, Phys. Rev. D81 (2010) 083537 [0911.4858]

    Pith/arXiv arXiv 2010

  35. [37]

    Seikel, C

    M. Seikel, C. Clarkson and M. Smith,Reconstruction of dark energy and expansion dynamics using Gaussian processes, JCAP 2012 (2012) 036 [1204.2832]

    Pith/arXiv arXiv 2012

  36. [38]

    Yahya, M

    S. Yahya, M. Seikel, C. Clarkson, R. Maartens and M. Smith,Null tests of the cosmological constant using supernovae, Phys. Rev. D89 (2014) 023503 [1308.4099]

    Pith/arXiv arXiv 2014

  37. [39]

    Zhao et al.,Dynamical dark energy in light of the latest observations, Nature Astron.1 (2017) 627 [1701.08165]

    G.-B. Zhao et al.,Dynamical dark energy in light of the latest observations, Nature Astron.1 (2017) 627 [1701.08165]

    Pith/arXiv arXiv 2017

  38. [40]

    R. C. Bernardo, D. Grandón, J. Said Levi and V. H. Cárdenas,Parametric and nonparametric methods hint dark energy evolution, Phys. Dark Univ.36 (2022) 101017 [2111.08289]

    Pith/arXiv arXiv 2022

  39. [41]

    Stern, R

    D. Stern, R. Jimenez, L. Verde, M. Kamionkowski and S. A. Stanford,Cosmic chronometers: constraining the equation of state of dark energy. I: H(z) measurements, JCAP 2010 (2010) 008 [0907.3149]

    Pith/arXiv arXiv 2010

  40. [42]

    Moresco et al.,Improved constraints on the expansion rate of the Universe up to z~1.1 from the spectroscopic evolution of cosmic chronometers, JCAP 2012 (2012) 006 [1201.3609]

    M. Moresco et al.,Improved constraints on the expansion rate of the Universe up to z~1.1 from the spectroscopic evolution of cosmic chronometers, JCAP 2012 (2012) 006 [1201.3609]

    Pith/arXiv arXiv 2012

  41. [43]

    Zhang, H

    C. Zhang, H. Zhang, S. Yuan, S. Liu, T.-J. Zhang and Y.-C. Sun,Four new observational H(z) data from luminous red galaxies in the Sloan Digital Sky Survey data release seven, Research in Astronomy and Astrophysics14 (2014) 1221 [1207.4541]

    Pith/arXiv arXiv 2014

  42. [44]

    Moresco,Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼ 2, Mon

    M. Moresco,Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼ 2, Mon. Not. Roy. Astron. Soc.450 (2015) L16 [1503.01116]

    Pith/arXiv arXiv 2015

  43. [45]

    Moresco, L

    M. Moresco, L. Pozzetti, A. Cimatti, R. Jimenez, C. Maraston, L. Verde et al.,A 6% measurement of the Hubble parameter atz ∼ 0.45: direct evidence of the epoch of cosmic re-acceleration, JCAP 05 (2016) 014 [1601.01701]

    Pith/arXiv arXiv 2016

  44. [46]

    A. L. Ratsimbazafy, S. I. Loubser, S. M. Crawford, C. M. Cress, B. A. Bassett, R. C. Nichol et al.,Age-dating Luminous Red Galaxies observed with the Southern African Large Telescope, Mon. Not. Roy. Astron. Soc.467 (2017) 3239 [1702.00418]

    Pith/arXiv arXiv 2017

  45. [47]

    Scolnic et al.,The Pantheon+ Analysis: The Full Data Set and Light-curve Release, Astrophys

    D. Scolnic et al.,The Pantheon+ Analysis: The Full Data Set and Light-curve Release, Astrophys. J. 938 (2022) 113 [2112.03863]

    Pith/arXiv arXiv 2022

  46. [48]

    Brout et al.,The Pantheon+ Analysis: Cosmological Constraints, Astrophys

    D. Brout et al.,The Pantheon+ Analysis: Cosmological Constraints, Astrophys. J. 938 (2022) 110 [2202.04077]

    Pith/arXiv arXiv 2022

  47. [49]

    Kazantzidis and L

    L. Kazantzidis and L. Perivolaropoulos,Evolution of thef σ8 tension with the Planck15/ΛCDM determination and implications for modified gravity theories, Phys. Rev. D 97 (2018) 103503 [1803.01337]. – 27 –

    Pith/arXiv arXiv 2018

  48. [50]

    DESI collaboration, DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations, JCAP 02 (2025) 021 [2404.03002]

    Pith/arXiv arXiv 2024

  49. [51]

    D. W. Hogg and D. Foreman-Mackey,Data analysis recipes: Using Markov Chain Monte Carlo, Astrophys. J. Suppl.236 (2018) 11 [1710.06068]

    Pith/arXiv arXiv 2018

  50. [52]

    G. L. Jones and Q. Qin,Markov chain monte carlo in practice, Annual Review of Statistics and Its Application9 (2022) 557 [https://doi.org/10.1146/annurev-statistics-040220-090158]

    doi:10.1146/annurev-statistics-040220-090158 2022

  51. [53]

    Sharma,Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy, Annual Review of Astronomy and Astrophysics55 (2017) 213 [1706.01629]

    S. Sharma,Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy, Annual Review of Astronomy and Astrophysics55 (2017) 213 [1706.01629]

    Pith/arXiv arXiv 2017

  52. [54]

    Medel-Esquivel, I

    R. Medel-Esquivel, I. Gómez-Vargas, A. A. M. Sánchez, R. García-Salcedo and J. Alberto Vázquez,Cosmological Parameter Estimation with Genetic Algorithms, Universe 10 (2024) 11 [2311.05699]

    Pith/arXiv arXiv 2024

  53. [55]

    R. C. Bernardo, E. A. Enriquez, R. Mendoza, R. Reyes and A. C. Velasco,Nature-inspired optimization, the Philippine Eagle, and cosmological parameter estimation, 2505.10299

    arXiv

  54. [56]

    R. C. Bernardo and Y. Chen,Genetic algorithm demystified for cosmological parameter estimation, 2505.10450

    arXiv

  55. [57]

    D. J. C. MacKay,Information Theory, Inference & Learning Algorithms. Cambridge University Press, USA, 2002

    2002

  56. [58]

    C. E. Rasmussen and C. K. I. Williams,Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). The MIT Press, 2005

    2005

  57. [59]

    C. M. Bishop and N. M. Nasrabadi,Pattern recognition and machine learning, vol. 4. Springer, 2006

    2006

  58. [60]

    R. M. Neal,Bayesian learning for neural networks, vol. 118. Springer Science & Business Media, 2012

    2012

  59. [61]

    Mukherjee, J

    P. Mukherjee, J. Levi Said and J. Mifsud,Neural network reconstruction of H’(z) and its application in teleparallel gravity, JCAP 12 (2022) 029 [2209.01113]

    Pith/arXiv arXiv 2022

  60. [62]

    Dialektopoulos, J

    K. Dialektopoulos, J. L. Said, J. Mifsud, J. Sultana and K. Z. Adami,Neural network reconstruction of late-time cosmology and null tests, JCAP 02 (2022) 023 [2111.11462]

    Pith/arXiv arXiv 2022

  61. [63]

    Benisty, J

    D. Benisty, J. Mifsud, J. Levi Said and D. Staicova,On the robustness of the constancy of the Supernova absolute magnitude: Non-parametric reconstruction & Bayesian approaches, Phys. Dark Univ. 39 (2023) 101160 [2202.04677]

    Pith/arXiv arXiv 2023

  62. [64]

    Escamilla-Rivera, J

    C. Escamilla-Rivera, J. Levi Said and J. Mifsud,Performance of non-parametric reconstruction techniques in the late-time universe, JCAP 10 (2021) 016 [2105.14332]

    Pith/arXiv arXiv 2021

  63. [65]

    Grandón and E

    D. Grandón and E. Sellentin,Bayesian error propagation for neural-net based parameter inference, Open J. Astrophys.5 (2022) astro.2205.11587 [2205.11587]

    Pith/arXiv arXiv 2022

  64. [66]

    Astrophys

    Astropy collaboration, Astropy: A Community Python Package for Astronomy, Astron. Astrophys. 558 (2013) A33 [1307.6212]

    Pith/arXiv arXiv 2013

  65. [67]

    Astropy collaboration, The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package, Astron. J. 156 (2018) 123 [1801.02634]

    Pith/arXiv arXiv 2018

  66. [68]

    Astropy collaboration, The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package*, Astrophys. J. 935 (2022) 167 [2206.14220]

    Pith/arXiv arXiv 2022

  67. [69]

    Pedregosa et al.,Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research 12 (2011) 2825 [1201.0490]

    F. Pedregosa et al.,Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research 12 (2011) 2825 [1201.0490]. – 28 –

    Pith/arXiv arXiv 2011

  68. [70]

    Wang, X.-J

    G.-J. Wang, X.-J. Ma, S.-Y. Li and J.-Q. Xia,Reconstructing Functions and Estimating Parameters with Artificial Neural Networks: A Test with a Hubble Parameter and SNe Ia, Astrophys. J. Suppl.246 (2020) 13 [1910.03636]

    Pith/arXiv arXiv 2020

  69. [71]

    Paszke et al.,PyTorch: An Imperative Style, High-Performance Deep Learning Library, 1912.01703

    A. Paszke et al.,PyTorch: An Imperative Style, High-Performance Deep Learning Library, 1912.01703

    Pith/arXiv arXiv 1912

  70. [72]

    Ferreira, T

    J. Ferreira, T. Barreiro, J. Mimoso and N. J. Nunes,Forecasting F(Q) cosmology withΛCDM background using standard sirens, Phys. Rev. D105 (2022) 123531 [2203.13788]

    Pith/arXiv arXiv 2022

  71. [73]

    Constraining f(Q) Cosmology with Standard Sirens

    J. Ferreira,Constraining f(Q) Cosmology with Standard Sirens, 2303.12674

    work page internal anchor Pith review Pith/arXiv arXiv

  72. [74]

    Testing $\Lambda$-Free f(Q) Cosmology

    J. Ferreira, T. Barreiro, J. P. Mimoso and N. J. Nunes,Testing Λ-free f(Q) cosmology, Phys. Rev. D 108 (2023) 063521 [2306.10176]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  73. [76]

    C. R. Harris et al.,Array programming with NumPy, Nature 585 (2020) 357

    2020

  74. [77]

    Virtanen et al.,SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nature Methods 17 (2020) 261

    P. Virtanen et al.,SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nature Methods 17 (2020) 261

    2020

  75. [78]

    J. D. Hunter,Matplotlib: A 2d graphics environment, Computing in Science & Engineering9 (2007) 90

    2007

  76. [79]

    Foreman-Mackey,corner.py: Scatterplot matrices in python, The Journal of Open Source Software 1 (2016) 24

    D. Foreman-Mackey,corner.py: Scatterplot matrices in python, The Journal of Open Source Software 1 (2016) 24

    2016

  77. [80]

    Moresco,Measuring the expansion history of the Universe with cosmic chronometers, 2412.01994

    M. Moresco,Measuring the expansion history of the Universe with cosmic chronometers, 2412.01994

    Pith/arXiv arXiv

  78. [81]

    Jimenez, L

    R. Jimenez, L. Verde, T. Treu and D. Stern,Constraints on the equation of state of dark energy and the Hubble constant from stellar ages and the CMB, Astrophys. J. 593 (2003) 622 [astro-ph/0302560]

    Pith/arXiv arXiv 2003

  79. [82]

    Simon, L

    J. Simon, L. Verde and R. Jimenez,Constraints on the redshift dependence of the dark energy potential, Phys. Rev. D71 (2005) 123001 [astro-ph/0412269]

    Pith/arXiv arXiv 2005

  80. [83]

    Jimenez and A

    R. Jimenez and A. Loeb,Constraining cosmological parameters based on relative galaxy ages, Astrophys. J. 573 (2002) 37 [astro-ph/0106145]

    Pith/arXiv arXiv 2002

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.