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Evidence for Log-Periodic Modulation in High-Redshift Compact Object Abundance Consistent with Cyclic Condensate Collapse

Takeshi Fukuyama

Abstract

We analyze the redshift distribution of high-$z$ galaxies and active galactic nuclei identified in early JWST data, and investigate the presence of periodic structure in the variable $x=\ln(1+z)$. A baseline-corrected unbinned frequency analysis reveals a statistically significant peak corresponding to a spacing $Δx \simeq 0.34$, suggesting an approximately log-periodic pattern in the redshift distribution. A periodic structure in $x$ implies a preferred scaling ratio in $(1+z)$, which may be interpreted as a realization of discrete scale invariance. We discuss the possibility that such behavior arises from cyclic condensate dynamics in Bose--Einstein condensate (BEC) cosmology. In the Fukuyama--Morikawa--Tatekawa framework, repeated collapse and re-formation episodes of a self-interacting condensate occur over characteristic timescales of order several $10^8$ years. When mapped into redshift space, this temporal periodicity naturally translates into an approximately constant spacing in $\ln(1+z)$. While the observed frequency is not interpreted as a sharp theoretical prediction, its magnitude is quantitatively consistent with the intrinsic cycle timescale of QCD-axion motivated condensate dynamics. The present analysis therefore provides observational support for cyclic BEC cosmology as a viable dynamical origin of log-periodic structure in the high-redshift universe.

Evidence for Log-Periodic Modulation in High-Redshift Compact Object Abundance Consistent with Cyclic Condensate Collapse

Abstract

We analyze the redshift distribution of high- galaxies and active galactic nuclei identified in early JWST data, and investigate the presence of periodic structure in the variable . A baseline-corrected unbinned frequency analysis reveals a statistically significant peak corresponding to a spacing , suggesting an approximately log-periodic pattern in the redshift distribution. A periodic structure in implies a preferred scaling ratio in , which may be interpreted as a realization of discrete scale invariance. We discuss the possibility that such behavior arises from cyclic condensate dynamics in Bose--Einstein condensate (BEC) cosmology. In the Fukuyama--Morikawa--Tatekawa framework, repeated collapse and re-formation episodes of a self-interacting condensate occur over characteristic timescales of order several years. When mapped into redshift space, this temporal periodicity naturally translates into an approximately constant spacing in . While the observed frequency is not interpreted as a sharp theoretical prediction, its magnitude is quantitatively consistent with the intrinsic cycle timescale of QCD-axion motivated condensate dynamics. The present analysis therefore provides observational support for cyclic BEC cosmology as a viable dynamical origin of log-periodic structure in the high-redshift universe.
Paper Structure (26 sections, 18 equations, 3 figures)

This paper contains 26 sections, 18 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Cyclic-collapse phenomenology and log-periodicity in $x=\ln(1+z)$
  3. Data
  4. Method: Baseline-corrected unbinned periodicity test
  5. Redshift variable
  6. Baseline model
  7. Baseline-corrected statistic
  8. Significance evaluation
  9. Scan versus fixed-frequency tests
  10. Results
  11. Fixed-frequency test
  12. Frequency scan
  13. Field contributions
  14. Robustness Tests
  15. Baseline modeling dependence
  16. ...and 11 more sections

Figures (3)

  • Figure 1: Null distribution of the baseline-corrected power at fixed $\omega=18.3$ for the combined multi-field sample. The vertical line indicates the observed value, corresponding to $p=2.5\times10^{-3}$.
  • Figure 2: Test-set $p$-values obtained in a 5-fold cross-validation analysis. In each fold, the frequency is selected from the training subset and evaluated on the held-out subset. The dashed line indicates $p=0.05$.
  • Figure 3: Distribution of $p$-values from repeated random train/test splits. The recurrence of low-$p$ realizations supports the robustness of the detected modulation.