Cosmological Parameter Tensions and Gravity

Cosmological “tensions” are not one phenomenon. A local distance ladder can disagree with a model-conditioned CMB inference; growth and lensing statistics can pull different parameter combinations; and a dark-energy extension can improve one data combination without identifying modified gravity. Through 2026-08-20, persistent discrepancies and evolving extension preferences warrant serious model tests, but they do not uniquely select new gravity. Independent calibrations, shared data, prior volume, supernova choice, and the distinction among DESI BAO, Lyα full shape, and galaxy full shape materially change the evidence balance.

Helpful background. Cosmological Inference and Model Appraisal supplies likelihood, posterior-predictive, tension-statistic, and model-comparison tools. This record applies them to current releases and asks when a discrepancy becomes evidence for gravity rather than calibration, matter content, or a phenomenological extension.

When a discrepancy points to gravity

The proposition has two requirements. First, a named discrepancy must persist after fixing data releases, calibration and selection covariance, cosmological model, parameter priors, and a prespecified statistic, preferably across substantially independent probes. Second, one predictive covariant gravity theory must improve the joint likelihood or held-out predictions without degrading other expansion, growth, lensing, or local tests. A posterior-mean separation or a preference inside $w_0w_a$CDM does not satisfy the second requirement.

Important axes are direct late-time calibration versus early model inference; data inconsistency versus ΛCDM inadequacy; parameter shift versus marginal evidence or predictive performance; shared anchors, sky, or calibration versus independence; background expansion versus growth and lensing; phenomenological dark energy versus modified gravity; and current product boundaries versus superseded combinations.

Assessment at 2026-08-20	Meaning
Question status	Open: discrepancies and model extensions remain under active data and methods revision
Evidence status	Contested: some combinations retain significant inconsistency or extension preference, while independent calibrations and newer products alter strength and interpretation
Confidence	Moderate; high that no unique gravity inference is established, moderate on the durability of each named tension
Domain	Planck 2018, ACT DR6.02, calibrated local ladders and JWST cross-checks, DESI DR2 BAO and Lyα full shape, and explicitly labeled DR1 galaxy/quasar full shape
What could change the conclusion	An independent CMB, ladder, supernova, or full-shape release; a common-systematic resolution; or a preregistered predictive gravity comparison

A starting project: reproduce one distance likelihood

Choose this topic if you enjoy statistical inference and can already compute FLRW distances, manipulate a covariance matrix, and distinguish a likelihood from a posterior. Start with the linked inference background, then read DESI Collaboration 2025, §§III.3 and V, Appendix B. Extract the measured distance combinations, effective redshifts, covariance convention, and systematic-error prescription before reading the dark-energy interpretation. The first question is whether your implementation describes the released distance measurements, not which new theory wins.

Use the DR2 BAO mean vector and covariance identified in the source map to implement the compressed Gaussian likelihood for one declared cosmological model. At a fixed parameter point, independently calculate the predicted distances and the quadratic residual. Check vector ordering, sound-horizon units, and covariance inversion; then reproduce one BAO-only parameter contour with the paper’s prior and parameter choices. Preserve the input files and environment. A laptop is sufficient for the distance calculation; a full CMB-plus-survey rerun needs the relevant likelihood software, more computing time, and an adviser who knows the data products.

The deliverable is a short methods note plus an executable likelihood and a baseline contour, with discrepancies traced to inputs or numerical error. A candidate extension is a controlled sensitivity study of one covariance or calibration assumption, with a held-out observable identified in advance. Check subsequent literature and official releases before treating that study as new research. If the baseline cannot be recovered, stop adding cosmological parameters and resolve the mismatch. If the proposed discriminator changes only a fitted background distance, narrow the claim to cosmological model comparison: identifying modified gravity also requires predictions for perturbations and independent tests.

What current probes actually establish

Planck’s primary temperature, polarization, and lensing likelihood under base ΛCDM tightly constrains an early-Universe model and derived late parameters. The likelihood choices, base model, and extensions are documented in §§2–7 and Tables 1–5 Planck Collaboration 2020, §§2–7. A derived Hubble constant is therefore not a direct local measurement; it inherits the model and foreground assumptions.

ACT DR6 supplies an independent telescope and high-resolution CMB pipeline. Its spectra, likelihood, ΛCDM results, and robustness tests are in §§2–8 of Louis et al. 2025, §§2–8. “ACT” combinations must still be unpacked because some chains import low-multipole polarization, WMAP, lensing, or BAO. Independence of the maps does not imply independence of every quoted chain.

The calibrated Cepheid–supernova ladder yields a persistently higher local expansion rate than base-ΛCDM CMB inference; anchors, Cepheids, supernovae, and the error budget are in §§2–6 and Tables 5–7 of Riess et al. 2022, §§2–6. JWST provides sharper cross-checks but not yet a single converged verdict. Freedman et al. compare TRGB, JAGB, and Cepheid routes in §§3–7 2024, §§3–7, while Riess et al. perform sample-matched tests in §§2–5 2024, §§2–5. Their anchors, hosts, and supernovae overlap even when methods differ.

Keep the three DESI products separate

DESI DR2 BAO is a distance-ruler analysis using galaxy, quasar, and Lyα BAO measurements. The estimators, tables, data combinations, and release products are given in pp. 4–16, Tables II–IV, and §X of the key paper DESI Collaboration 2025, pp. 4–16 and §X. Preferences for an extension depend on which CMB and supernova likelihoods are added; BAO alone is not a detection of modified gravity.

The July 2026 DESI DR2 Lyα result is a separate full-shape and Alcock–Paczyński analysis of the Lyα auto-correlation and its cross-correlation with quasars. Its measurement and cosmological interpretation are in §§2–7 DESI Collaboration 2026, §§2–7. The companion validation uses hundreds of mocks, blinded splits, and analysis variations; BAO and AP pass its requirements, but the proposed $f\sigma_8$ estimator is biased in mocks and is excluded from the final analysis Herbold et al. 2026, §§3–6 and conclusion. No current growth claim should be inherited from that rejected estimator.

Galaxy and quasar full-shape information remains a DR1 product. Analyses combining it with newer distances are explicitly “DR1 full shape plus DR2 BAO” Forero-Sánchez et al. 2026, title, abstract, and §§2–5. Calling those chains “DR2 galaxy full shape” would merge different releases and covariances.

Results and open questions at 2026-08-20

Claim or evidence	What it supports	What it does not establish
Planck and ACT CMB consistency	A robust early-Universe ΛCDM baseline across independent instruments	A direct local expansion measurement or complete chain independence
Calibrated local ladder	A persistent early/late expansion discrepancy under specified anchors and Cepheid–SN modeling	The physical cause or a unique gravity modification
JWST TRGB, JAGB, and Cepheid comparisons	Powerful tests of crowding, sample, and calibration systematics	A mature precision consensus from independent hosts and anchors
DESI DR2 BAO	Precise distance–redshift information and conditional extension tests	Galaxy full-shape growth or direct evidence for gravity
DESI DR2 Lyα full shape/AP	An updated high-redshift broadband AP measurement	A validated $f\sigma_8$ measurement; that estimator was excluded
DR1 galaxy/quasar full shape plus DR2 BAO	A controlled cross-release combination with modeled covariance	A DR2 galaxy full-shape product

The strongest evidence is not a paper count but the persistence or movement of a discrepancy under genuinely independent data and prespecified choices. Shared supernovae, anchors, sky, external low-multipole likelihoods, and DESI tracers must be represented in the covariance and interpretation.

Competing interpretations and the missing discriminator

The new-gravity interpretation says that recurring early/late and expansion/growth discrepancies indicate that the background and perturbation equations are incomplete. Its strongest form is predictive: one theory should link the background distance shift to lensing, growth, gravitational-wave propagation, and local screening.

The systematics interpretation notes that ladder results move with anchors, sample construction, crowding, and covariance, while cosmological extension preferences move with supernova compilation and DESI product. The model-flexibility interpretation adds that $w_0w_a$CDM is phenomenological; a better fit does not identify an extra gravitational degree of freedom. The unresolved discriminator is a theory-specific, blinded prediction that succeeds in an independent probe not used to tune it.

Counterexamples, null results, and failed routes

The DESI Lyα validation is a concrete failed route: an apparently informative growth estimator was not promoted after mock bias was found. It narrows what the full-shape release establishes without discrediting the validated AP result. JWST disagreement is another warning against treating a new instrument as automatic independence when hosts, anchors, and supernovae overlap.

A common failed route is to compare sigma values computed with different data vectors, covariances, or parameter priors. Another is to turn a phenomenological dark-energy preference into a gravity claim without checking perturbations and theoretical health. Conversely, broad CMB agreement does not prove that every late-time calibration is wrong; it confirms the conditional early baseline.

What would change the assessment

The record would move toward supported new physics if a discrepancy repeated in an independent release and a preregistered gravity theory improved expansion, growth, and lensing jointly while satisfying local and gravitational-wave constraints. It would weaken if a shared calibration or selection effect reconciled the same objects across methods, or if a new likelihood removed the extension preference under unchanged analysis choices. A validated DESI growth estimator or a public galaxy/quasar DR2 full-shape release would open a genuinely new row rather than modify the current ones by relabeling.

Research checklist

• Name the tension, data releases, likelihood tags, calibration, and statistic before quoting significance.
• Draw a dependency graph for shared anchors, supernovae, sky, external CMB likelihoods, and DESI tracers.
• Separate direct measurements from parameters inferred under a cosmological model.
• Recompute results under declared prior measures and report predictive or evidence statistics, not only posterior shifts.
• Keep DESI DR2 BAO, DR2 Lyα full shape/AP, and DR1 galaxy/quasar full shape as distinct products.
• Exclude the Lyα $f\sigma_8$ estimator from final inference unless a later validated product supersedes the 2026 decision.
• Test a gravity theory against held-out growth, lensing, propagation, and local constraints.
• Publish chains, covariance, nuisance settings, sampler diagnostics, and exact software revisions.

Source and data map

Planck and ACT provide the early CMB baseline; Riess et al. provide the calibrated distance ladder; Freedman et al. and Riess et al. provide contrasting JWST checks. DESI DR2 BAO is pinned to arXiv:2503.14738v3 / Physical Review D 112, 083515. DESI DR2 Lyα full shape is arXiv:2607.27410v3 with validation arXiv:2607.27411v2. Forero-Sánchez et al. explicitly delimit the DR1 full-shape plus DR2 BAO combination.

Official DR2 BAO tables, covariance, and chains are documented in the Y3 BAO/cosmology README; the listed CobayaSampler/bao_data revision is bb0c1c9009dc76d1391300e169e8df38fd1096db. NASA LAMBDA ACT DR6.02 separates maps, beams, PSPIPE spectra and likelihoods, and chains. No joint rerun was performed. A public July-2026 Lyα full-shape chain archive with a durable checksum was not verified, so the papers define that product boundary.

References

• DESI Collaboration. 2025, “DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints,” Physical Review D 112, 083515, arXiv:2503.14738v3, DOI 10.1103/tr6y-kpc6.
• DESI Collaboration. 2026, “DESI DR2 Results IV: Alcock–Paczyński Measurements from the Lyman Alpha Forest and Cosmological Constraints,” arXiv:2607.27410v3, arXiv.
• Forero-Sánchez, D., et al. 2026, “Cosmological Constraints from a Joint DESI DR1 Full-Shape and DR2 BAO,” arXiv:2602.18761v1, arXiv.
• Freedman, W. L., et al. 2024, “Status Report on the Chicago–Carnegie Hubble Program (CCHP): Measurement of the Hubble Constant Using the Hubble and James Webb Space Telescopes,” arXiv:2408.06153v3, arXiv.
• Herbold, M., et al. 2026, “Validation of the DESI DR2 Lyα Forest Full-Shape Analysis,” arXiv:2607.27411v2, arXiv.
• Louis, T., et al. 2025, “The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and ΛCDM Parameters,” arXiv:2503.14452v2, arXiv.
• Planck Collaboration. 2020, “Planck 2018 Results. VI. Cosmological Parameters,” Astronomy & Astrophysics 641, A6, DOI 10.1051/0004-6361/201833910.
• Riess, A. G., et al. 2022, “A Comprehensive Measurement of the Local Value of the Hubble Constant,” Astrophysical Journal Letters 934, L7, DOI 10.3847/2041-8213/ac5c5b.
• Riess, A. G., et al. 2024, “JWST Observations Reject Unrecognized Crowding of Cepheid Photometry as an Explanation for the Hubble Tension,” Astrophysical Journal 977, 120, DOI 10.3847/1538-4357/ad8c21.