review reclassification. The previously-reported 2.9–4\(\sigma\) tension between canonical \(t_{\rm univ} = 12.69\) Gyr and HD140283 13.5 ± 0.2 Gyr used Bond 2013 statistical-only uncertainty. Modern systematic-aware uncertainty (Joyce & Tayar 2023; Valle 2024) gives \(\sigma_{\rm total} \sim 0.5\) Gyr → 1.62\(\sigma\) SOFT; the GC ensemble (Cimatti & Moresco 2023) 13.0 ± 0.4 Gyr → 0.77\(\sigma\) PASS. See /updates/.

Observable detail · COSMOLOGY

Age of universe \(t_{\rm univ}\)

Cosmic age under the corpus-canonical constant-\(P_0\) treatment.

Amendment — page reverted. An earlier version of this page reported 13.7 Gyr / 0.9σ HIT under a temporal Avrami profile \(P(z) = P_0 + (1-P_0)\exp(-t(z)/t_{50})\) with \(t_{50} \approx 1.5\) Gyr. That profile is not derived from the canonical Brans–Dicke + Gross–Pitaevskii action (DCT_00 line 323: "the Parrott field has been at its equilibrium value \(P_0\) since \(t \sim 10^{-39}\) s") and was reverted across the cluster papers and the public site (S17 No-Go: temporal P(z) reframings violate Jensen's inequality on the BD action). The headline canonical answer is the constant-\(P_0\) value and the residual tension below. The Avrami branch is preserved as a clearly-labelled diagnostic block at the bottom of this page. See Updates.
Prediction (canonical, constant-\(P_0\))\(t_{\rm univ} \approx 12.69\) Gyr (Friedmann integration with global \(t \to t/\sqrt{P_0}\) rescaling, \(P_0 = 0.851\), \(H_0 = 67.4\) km/s/Mpc, \(\Omega_m = 0.315\), \(\Omega_\Lambda = 0.685\))
Measured (HD140283, Bond 2013)\(13.5 \pm 0.2\) Gyr — the oldest stellar-age constraint with public, independently-reproducible isochrone fitting
Residual\(|t_{\rm univ}^{\rm DCT} - t_{\rm HD140283}| / \sigma_{\rm HD140283} = (13.5 - 12.69) / 0.2 = 4.05\sigma\) (HD140283 alone); ~2.9\(\sigma\) when combined with the Hubble systematic envelope (\(\sigma_{\rm comb}\) from Cepheid/TRGB H\(_0\) tension)
Statussoft — real tension; one of the corpus's standing open items in the cosmology cluster
Source paperDCT-COS-01

Mechanism

Under the canonical conformal-frame mapping \(\tilde g_{\mu\nu} = P\,g_{\mu\nu}\) with \(P = P_0 = 0.851\) constant from BBN to today (per DCT_00), background distances and timescales rescale by \(\sqrt{P_0}\). The cosmic age computed in the physical (Jordan) frame is \(t_{\rm univ}^{\rm DCT} = t_{\rm univ}^{\Lambda{\rm CDM}} \cdot \sqrt{P_0}\). With \(t_{\rm univ}^{\Lambda{\rm CDM}} = 13.797\) Gyr (Planck 2018) and \(\sqrt{0.851} = 0.9225\), the canonical DCT prediction is \(t_{\rm univ} = 13.797 \cdot 0.9225 = 12.728\) Gyr; the explicit Friedmann-integral re-derivation in dct_gc_age_resolution.py gives \(12.69\) Gyr.

Derivation chain

  1. Canonical action: Brans–Dicke + Gross–Pitaevskii with the conformal-frame mapping \(\tilde g = P g\); \(P\) is spatially and temporally constant at cosmological scales (DCT_00 line 323).
  2. FRW background under the rescaling: \(H_{\rm phys}(z) = H_E(z)/\sqrt{P_0}\); cosmic age integrates as \(t_{\rm univ}^{\rm DCT} = \sqrt{P_0} \cdot t_{\rm univ}^{\Lambda{\rm CDM}}\).
  3. Substituting \(P_0 = 0.851\) and \(t_{\rm univ}^{\Lambda{\rm CDM}} = 13.80\) Gyr → \(t_{\rm univ}^{\rm DCT} = 12.73\) Gyr (analytic) or \(12.69\) Gyr (Friedmann integration).
  4. Compared to HD140283 \(13.5 \pm 0.2\) Gyr → 4.0\(\sigma\) tension on the bare HD140283 envelope, ~2.9\(\sigma\) with the Hubble systematic combination per the published cosmology companion audits.

Methodology

Python verification

The verification script for this observable is dct_gc_age_resolution.py. The constant-\(P_0\) branch (lines that integrate the Friedmann equation with global \(\sqrt{P_0}\) rescaling) reproduces 12.69 Gyr; the script also contains a non-canonical Avrami branch that is explicitly noted in its header as reverted per the amendment. Run with python3 dct_gc_age_resolution.py.

Diagnostic — non-canonical temporal Avrami branch (reverted)

Show the reverted Avrami branch (kept for reproducibility of the older claim only)

Under a temporal profile \(P(z) = P_0 + (1 - P_0) \exp(-t_{\rm lookback}(z) / t_{50})\) with \(t_{50} \approx 1.5\) Gyr (and \(n = 4\) in the more general fitted form), the Friedmann integration recovers \(t_{\rm univ} = 13.65\) Gyr → 0.7\(\sigma\) consistency with HD140283.

Per the canonical Brans–Dicke + Gross–Pitaevskii action plus 600-cell Allen–Cahn kinetics. The corpus has only two valid Avrami profiles, both spatial: \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) (galactic, in DCT-DM-01) and \(P(N) = 1 - \exp(-N/N_0)\) (popularisation pipeline, not part of the cluster papers). A temporal P(z) at cosmological scales contradicts DCT_00's "frozen at \(P_0\) since \(t \sim 10^{-39}\) s" statement. The branch is shown here only for reproducibility of the older 13.7 Gyr / 0.9\(\sigma\) reading; it does not constitute a DCT prediction.

If a temporal P(t) treatment can be derived from the canonical action plus Allen–Cahn kinetics in future work, the GC-age tension would naturally relax. Until then the constant-\(P_0\) ~2.9–4.0\(\sigma\) tension stands.

Audit notes

Reconciliation against the corpus audits (D6)

Per the May 2026 amendment log and public site update, an earlier version of this page used the reverted temporal Avrami branch as its headline. The canonical answer is the constant-\(P_0\) value (~2.9–4.0\(\sigma\) tension). The Avrami branch is preserved here only as a labelled diagnostic.

References

Back to all observables or the predictions table.