Deterministic chaos in the large-scale universe: data versus speculations

TL;DR

This paper analyzes cosmic microwave background and galaxy distribution spectra, revealing exponential decay patterns and signs of chaotic dynamics, with more complex chaos observed in large galaxy surveys, suggesting a universal chaotic mechanism in the universe.

Contribution

It demonstrates the presence of exponential decay and chaotic features in cosmological spectra, linking these patterns to underlying chaotic dynamics in the universe.

Findings

Exponential decay observed in CMB and galaxy spectra.

Waviness with consistent periods indicates chaotic mechanisms.

Distributed chaos leads to a stretched exponential form in large surveys.

Abstract

It is shown, that the both angular CMB Doppler spectrum: $C_l$ (Planck space telescope - cosmic microwave background [1]) and the 3D galaxy-galaxy power spectrum: $P(k)$ (Sloan Digital Sky Survey SDSS-II [2]), exhibit a considerable range with an exponential decay: $370 < l < 2500$ and $0.05 < k < 0.27~~(h/Mpc)$, respectively. The rates of the exponential decay are $l_c \simeq 300$ for $C_l \sim \exp-(l/l_c)$ and $k_c \simeq 0.09~~(h/Mpc)$ for $P(k) \sim \exp-(k/k_c)$. A waviness is observed along a straight line representing the exponential decay in the log-linear scale graphs of these spectra. In both cases the waviness has period (distance between peaks) equal to the same $l_c$ and $k_c$ as for the exponential decay. It means that the waviness is generated by the same, presumably chaotic, mechanism that generates the exponential decay. A more complex, distributed, chaos is observed in the Baryon Oscillation Spectroscopic Survey (the largest component of the SDSS-III containing nearly one million galaxies) [3]. In this case the $P(k)$ spectrum is a weighted superposition of the exponentials. At assumption that dynamics of the dispersive waves, driving the distributed chaos, is dominated by the effects of a surface tension this weighted superposition of the exponentials is converged to a compact form of a stretched exponential $P(k) \sim \exp-(k/k_b)^{1/2}$, in good agreement with the data.