A Chronovibrational Hypothesis on the Hubble Constant Tension

A Chronovibrational Hypothesis on the Hubble Constant Tension Paolo Giordana Independent Researcher, Italy [email protected] October 17, 2025 1 Introduction: the Hubble Tension and Recent Works The so-called Hubble constant tension H0is one of the most debated issues in cosmology. Local measurements (Cepheids, Tip of the Red Giant Branch,Surface Brightness Fluctuations) tend to yield higher values (H0≃73–74 km s−1Mpc−1), while global estimates from the CMB (e.g. Planck) indicate a lower value (H0= 67.4±0.5 km s−1Mpc−1). The discrepancy is now beyond 5σ, hinting at unknown systematics or new physics beyond ΛCDM. Several recent studies have investigated this tension with Cepheid-independent methods: •Blakeslee et al. (2021):H0= 73.3±0.7 (stat) ±2.4 (sys) km s−1Mpc−1from SBF distances.1 •Anand et al. (2024): TRGB method with JWST for Fornax, anchoring the SBF scale with uncertainty <2%.2 •Anand et al. (2025): extension to the Virgo cluster, confirming a high value of H0.3 •Jensen et al. (2025): SBF calibration via TRGB, H0= 73.8±0.7 (stat) ±2.3 (sys).4 These works suggest a possible correlation between the measured value of H0and redshift z: low-zmeasurements tend to be higher, high-zlower. This does not necessarily imply an intrinsic variation of H0; it may reflect local metric effects or yet-unaccounted physics. The chronovibrational model offers an interpretation in terms of coherence/decoherence of a temporal field. 2 Chronovibrational Hypothesis Time is modeled not as a mere coordinate but as a global quantum harmonic field ψ(t), subject to damping and oscillation: ψ(t) = A e−Λ(t)tcos(Ωt+ϕ), where Ais an amplitude, Λ(t) a (possibly time-dependent) damping, Ω a fundamental frequency and ϕa phase. 1J. P. Blakeslee et al., The Hubble Constant from Infrared Surface Brightness Fluctuation Distances, arXiv:2101.02221. 2G. S. Anand et al., A Tip of the Red Giant Branch Distance to the Fornax Cluster with JWST, arXiv:2405.03743. 3G. S. Anand et al., Resolving the Virgo Cluster with JWST, arXiv:2408.16810. 4J. B. Jensen et al., The TRGB-SBF Project. III. Refining the HST SBF Distance Scale Calibration with JWST, arXiv:2502.15935. 1 2.1 Critical Function and Temporal Coherence With a latency t0(to regularize t→0), define fcrit(t) = e−Λ(t) (t+t0)cos[Ω(t+t0)] p1−e−2Λ(t) (t+t0), where: •Λ(t): damping coefficient [s−1], •Ω: angular frequency [rad s−1], •t0: latency [s], e.g. t0∼ℏ/Ethreshold 1q. This fcrit quantifies the intensity of harmonic instabilities. Metric stability is encoded in the harmonic factor Γharm(t) = expβ τ∗Zt t0 f2 crit(τ)dτ, where βis dimensionless and τ∗is a characteristic time scale (chosen below) so the exponent is dimensionless. The coherence functional F[ψ(t)] = exp − ¨ ψ(t) Ω2ψ(t)!2  is made dimensionless using Ω as normalization scale (a gauge-like choice ensuring F∈(0,1]). 2.2 Cosmological Interpretation (Inference vs Dynamics) The difference between local and global measurements of H0is modeled as an apparent effect: cumulative decoherence along the line of sight alters the inference of distances/velocities, not the FRW dynamics. We therefore treat Γharm(z) as a post-processing factor on observables, avoiding double-counting with background expansion. 2.3 Example: Rotational Anisotropy of Galaxies In the GOODS-S field of JADES5one finds N⟳= 158, N⟲= 105, p ≃7×10−4(∼3.4σ). Defining A(z) = N⟳−N⟲ N⟳+N⟲ , one observes A(z < 1) ≈0.12, A(z > 2) ≈0.20. Within this model, larger harmonic instability at high zcould leave a persistent anisotropic imprint. (This is suggestive, not proof.) Simulations Standard IllustrisTNG gives A(z)≈0. Injecting chronovibrational perturbations via fcrit produces a growing trend compatible with the indication above. 5L. Shamir, The distribution of galaxy rotation in JWST Advanced Deep Extragalactic Survey, 2025. 2 2.4 Summary Chronovibration pictures the universe as a dissipative harmonic system where matter, energy, and geometry are modes of ψ(t). It may offer a unifying key for the Hubble tension and other anomalies. 3 Physical Explanation and Chronovibrational Calculation Perturbations of coherence manifest through fcrit(t), controlled by Λ(t) and a latency t0. 3.1 Effect on the Hubble Constant (Apparent) We model an apparent correction Heff 0(z) = v deff(z)=H0·Γharm(z), interpreting Γharm as an inference modifier (not a change in FRW). For z≪1, this reduces to a rigorous rescaling of the linear Hubble law. 3.2 Harmonic Factor, Integration, and Mapping t(z) We adopt the cosmic time scale τ∗≡H−1 0: Γharm(z) = exp"β τ∗Zt(z) t0 f2 crit(t′)dt′#, τ∗=H−1 0. For flat ΛCDM with H(z) = H0pΩm(1 + z)3+ ΩΛand ΩΛ= 1 −Ωm, dt dz =−1 (1 + z)H(z), t(z) = Z∞ z dz′ (1 + z′)H(z′). This gives the t↔zmapping needed to integrate f2 crit once Λ(t) is specified (e.g. constant, or a power law in a). 3.3 Small-Effect Expansion (Data-Fit Friendly) For modest departures from unity, expand Γharm(z)≃1 + βI(z) + O(I2),I(z)≡1 τ∗Zt(z) t0 f2 crit(t′)dt′. Hence the apparent shift obeys Heff 0(z) H0 −1≃βI(z). This linearized form is convenient for fitting multiple distance indicators simultaneously (TRGB, SBF, SN Ia) without altering the FRW background. 3.4 Numerical Order-of-Magnitude Bridging HCMB 0≃67.4 to Hloc 0≃73.0 requires Γharm(zlow) Γharm(zhigh)≈73.0 67.4≈1.083. If βis constant, I(zlow)− I(zhigh)≈0.08 is sufficient at order of magnitude to reproduce the ratio. A realistic estimate needs an explicit Λ(t) and a multi-probe fit. 3 4 Conclusions and Perspectives The chronovibration hypothesis is a theoretical, speculative framework for the Hubble tension. In this view, the observed difference between local and global H0values is an apparent effect of cumulative temporal decoherence of ψ(t) along the line of sight; FRW dynamics remain unmodified. The factor Γharm(z) then acts as a redshift-dependent inference correction. There is currently no direct observational evidence for ψ(t) or for a physical fcrit(t). The increase in rotational anisotropy with redshift is compatible with this framework but not probative. Absence of Contradiction. A larger anisotropy at high ztogether with a smaller apparent H0can both arise as traces of primordial harmonic instability: •ancient galaxies preserve a directional imprint (A(z) increasing with z); •distance inferences accumulate decoherence along the path, reducing Γharm(z) at high z. Future Perspectives. Tests include: 1. fitting Heff 0(z) vs. zwith TRGB/SBF/SN Ia under the linearized model, 2. measuring A(z) on widened samples and checking consistency with a chosen Λ(t). In summary, while unconfirmed, chronovibration yields a falsifiable link between the Hubble tension and rotational anisotropy. A consistent use of the normalized integral and a strict separation between inference corrections and FRW dynamics prevent double counting and enable empirical tests. 4