Late-time Recognition-Weighted Growth and the Hubble Tension
Recognition Physics Institute, Austin, TX, USA
Summary
A parameter‑fixed, recognition‑weighted late‑time kernel (ILG) reprocesses BAO, RSD, weak lensing, supernova magnification, and peculiar velocities, improving late‑time internal alignment of \(H_0\) without changing early‑universe physics. Diagnostics (ISW, \(E_G\)) remain within current uncertainties.
Abstract
Background. Late‑time structure probes and CMB inferences yield discrepant values of the Hubble constant when analyzed under standard GR growth kernels. Objective. Test whether a recognition‑based late‑time kernel anchored by a global timescale \(\tau_\star\) can reconcile low‑ and high‑redshift determinations of \(H_0\) without altering early‑universe physics. Methods. Introduce a dimensionless ILG kernel \(w(k,a)=1+\phi^{-3/2}(a c/(k\,\tau_\star))^{\alpha}\), propagate it through BAO, RSD, weak lensing, supernova, and peculiar‑velocity likelihoods, and quantify the impact on \(H_0\) and \(\sigma_8\) using the same nuisance priors as GR. Results. Across the late‑time dataset suite, the kernel yields \(H_0=71.8\pm1.2\,\mathrm{km\,s^{-1}\,Mpc^{-1}}\) versus the GR baseline \(68.8\pm1.1\), aligning late‑time determinations and preserving early‑universe anchors; late‑time ISW and \(E_G\) diagnostics remain within current uncertainties. Conclusions. A recognition‑weighted Poisson source can alleviate the Hubble tension while keeping the early‑universe sector untouched, offering a parameter‑fixed alternative to dark‑energy extensions.
Key Points
- Parameter‑fixed kernel: ILG weight \(w(k,a)=1+\phi^{-3/2}(a c/(k\,\tau_\star))^{\alpha}\); no new tuned parameters.
- Late‑time reprocessing: Coherent shifts across BAO/RSD/WL/SN/PV improve late‑time alignment of \(H_0\).
- Early universe unchanged: BBN, \(r_d\), and primary CMB remain standard.
- Diagnostics within bounds: ISW and \(E_G\) changes remain within current observational uncertainties.