Dark Energy, the Hubble Tension, and Low-Frequency Diagnostics

Bys: Li, Longji and Li, Kaisheng

This volume develops an EQT reinterpretation of the Hubble tension as an extrapolation problem rather than a simple conflict between two measurements of the same quantity. Its central question is precise: why do early-universe and late-universe routes to the Hubble constant differ by roughly five standard deviations, and does the discrepancy lie in measurement or in extrapolation? The book accepts cosmological redshift as expansion and treats ΛCDM as an empirically successful reference framework. It does not set up ΛCDM or early-dark-energy models as failed targets. Instead, it asks whether the tension may arise because the early-universe route extrapolates through a late-time dark-energy transition band that the constant-Λ assumption does not represent.
The methodological starting point is the distinction between two quantities: (H_0 {\rm early}), inferred from CMB data by fitting an early-universe state and extrapolating it to (z=0), and (H_0 {\rm late}), read directly from the local distance ladder. In the standard presentation these are treated as two measurements of one number. Here they are endpoints of different operations. The late route is a near-present readout; the CMB route is an extrapolated endpoint. They should agree only if the expansion history used in the extrapolation is complete from recombination to the present.
The proposed EQT reading is that the true late-time expansion history contains a transition band in the ultra-low-frequency dark-energy sector, shared with the companion volume on dark-energy projection readout. In that band, (w(z)) departs from (-1). A ΛCDM extrapolation assumes (w=-1) and therefore passes through the same interval while omitting the transition. The omitted segment is accumulated by the extrapolation integral and appears at the endpoint as a systematic shift in (H_0). The observed difference between (H_0 {\rm early}) and (H_0 {\rm late}) is thus reinterpreted as the endpoint consequence of a missing late-time transition term, not as a direct contradiction between two local measurements.
The book proceeds from object foundations to transition-band localization, extrapolation integrals, consistency checks, and falsifiable joint predictions. It identifies the transition-band center with the matter-dark-energy equality scale, around (z\sim0.33), while treating the band width cautiously because its precise boundary depends on the unfinished weighting structure of the ultra-low-frequency window. It then uses the observed Hubble tension as an input to reverse-calibrate the transition amplitude, emphasizing that this is a scale-consistency test, not a parameter-free prediction of the numerical value of the tension.
The decisive test is joint constraint. The transition band invoked here must be the same one used in the dark-energy projection-readout volume: the same redshift interval and effective amplitude must account both for the endpoint shift in (H_0) and for localized residuals in the expansion history. This two-window requirement distinguishes the proposal from ΛCDM, which contains no transition band, and from early-dark-energy models, which intervene near recombination rather than in the late-time (z\sim O(1)) regime.
The volume is deliberately constrained. It does not introduce new EQT postulates, does not claim to predict the (5.6, {\rm km, s {-1}, Mpc {-1}}) gap from first principles, and does not claim that the transition amplitude has already been derived from a completed microphysical weighting function. Its contribution is to recast the Hubble tension as a diagnostic of extrapolation, connect it to the same late-time transition band that appears in dark-energy projection readout, and specify clear conditions under which this interpretation would fail.

• Format: Paperback
• Language: English
• ISBN: B0H6DV4HWC
• ISBN13: 9798183823332
• Release Date: June 2026
• Publisher: Independently Published
• Length: 146 Pages
• Weight: 0.41 lbs.
• Dimensions: 0.4" x 6.0" x 9.0"