Hubble Tension Statistical Comparison Explorer

Quantify the Gaussian σ-tension, sound-horizon shift Δr_d, and cosmic age impact between any two H₀ determinations.

Epistemic Status: Competing InterpretationsSection: Interactive ExplorersReviewed:
Core Physical Relation

Given two independent measurements H₀,₁ ± σ₁ and H₀,₂ ± σ₂, their statistical discrepancy in Gaussian standard deviations is T_σ = |H₀,₁ − H₀,₂| / √(σ₁² + σ₂²). Comparing Planck 2018 (67.36 ± 0.54 km/s/Mpc) and SH0ES 2022 (73.04 ± 1.04 km/s/Mpc) yields an 8.4% difference with T_σ = 4.85σ (or >5.0σ in full joint likelihood fits).

Interactive Physics Calculator

Two Independent H₀ Determinations (km/s/Mpc)
Gaussian Tension T_σ4.85 σΔH₀ = 5.68 km/s/Mpc (+8.4%)
Implied Cosmic Age (Ω_m=0.315)13.79 vs 12.72 GyrSN Ia shift ΔM = 0.18 mag
Required Sound Horizon r_d135.7 Mpcvs 147.1 Mpc standard ΛCDM

Governing Equation & Worked Benchmark

Gaussian Tension Metric & Implied Flat-ΛCDM Cosmic Age

T_σ = |H₀,A − H₀,B| / √(σ_A² + σ_B²) ; t₀(H₀, Ω_m) = (977.8 Gyr / H₀) · (2 / 3√Ω_Λ) ln[ (1 + √Ω_Λ) / √Ω_m ]

At fixed matter fraction Ω_m = 0.315, cosmic age scales inversely with H₀: shifting H₀ from 67.4 to 73.0 km/s/Mpc lowers t₀ from 13.79 Gyr to 12.73 Gyr unless Ω_m also decreases.

Benchmark StepPhysical Details & Result
ScenarioCompare Planck 2018 CMB (H₀ = 67.36 ± 0.54 km/s/Mpc) against SH0ES 2022 Cepheid+SN Ia (H₀ = 73.04 ± 1.04 km/s/Mpc).
CalculationDifference ΔH₀ = 5.68 km/s/Mpc (+8.43%). Combined uncertainty σ_comb = √(0.54² + 1.04²) = 1.172 km/s/Mpc. Tension T_σ = 5.68 / 1.172 = 4.85σ. Reconciling them via the early-universe sound horizon requires shrinking r_d from 147.1 Mpc to 147.1 × (67.36 / 73.04) = 135.7 Mpc (−7.8%).
Physical TakeawayNeither a single calibration systematic nor a trivial tweak to late-time dark energy easily absorbs an 8.4% shift without altering either the sound horizon r_d or local SN Ia luminosities by ~0.18 mag.

Physical Mechanism & Interpretation

This explorer lets you select presets from major cosmological collaborations (Planck 2018, ACT DR4/DR6, DESI BAO+BBN, CCHP JWST TRGB/JAGB, SH0ES 2022, and TDCOSMO strong lensing) or enter custom H₀ ± σ values and matter density Ω_m.

It simultaneously computes the Gaussian σ discrepancy, equivalent magnitude offset ΔM = 5 log₁₀(H₀,A / H₀,B), required sound-horizon rescaling Δr_d / r_d, Hubble time T_H = 1/H₀, and integrated flat-ΛCDM age of the universe t₀.

Model Assumptions & Systematic Uncertainties

Simple 1D Gaussian quadrature T_σ assumes the two probes share no correlated calibration anchors; comparing two local ladders that share Gaia parallaxes or NGC 4258 requires subtracting their shared anchor covariance.

Related Concepts & Methods

Scientific Sources & Provenance

  1. Planck 2018 Cosmological Parameters (PR3) (PR3 (2020 A&A 641, A6)) — Planck Collaboration, Aghanim, N., et al. 2020, A&A, 641, A6. Archive / Reference ↗
  2. SH0ES Local Distance Ladder Hubble Constant (2022 Baseline Cepheid + SN Ia) — Riess, A. G., et al. 2022, ApJL, 934, L7 (A Comprehensive Measurement of the Local Value of the Hubble Constant). Archive / Reference ↗
  3. JWST / MAST Science Archive & Mission Documentation (Cycle 1–4 Public Releases (2022–2026)) — Rigby, J., et al. 2023, PASP, 135, 048001 (The Science Performance of JWST as Characterized in Commissioning). Archive / Reference ↗
  4. ESA Gaia Archive — Data Release 3 (DR3 (2022-06-13)) — Gaia Collaboration, Vallenari, A., et al. 2023, A&A, 674, A1 (Gaia Data Release 3). Archive / Reference ↗