Cyclic universe and the Self-Organized Criticality concept

https://orcid.org/0000-0001-8442-7973

Cyclic universe and the Self-Organized Criticality concept

Abstract

Sandpile Paradigm was proposed by Bak, Tang and Wiesenfeld [1] to explain simple model of Self- Organized Criticality (SOC). When the sand fall on the sandpile (input: driver), we will see, that at some critical point (reaching adequate angle), sand will slide down to get the saturation phase. Here the gravity plays the energy input role. This short paper annouces that the cyclic universe could be treated as a SOC system.

SOC systems

We can conclude that for earthquakes phenomenon energy input is tectonic stressing, criticality (instability threshold) is the dynamical friction and energy output is the rupture area. In astrophysics, for example, magnetospheric substorms exhibits itself as a SOC systems. Solar wind plays the energy input role, magnetic reconnection is the instability threshold (criticality) and auroral bursts are the intermittent avalanches (output)[2]. The SOC approach has been already used for interpretation of magnetospheric processes and recently for the Earth’s Auroral Kilometric Radiation [3,4]. Data gathered by the POLRAD swept frequency radiospectrograph (Interball–2 mission) have been used for a preliminary analysis of a number of short bursts of the Auroral Kilometric Radiation (AKR) as a function of their intensity.

Key Features of SOC Systems

1. Scale-Invariance: SOC systems exhibit events (or avalanches) of various sizes, from very small to very large, without a characteristic scale. This produces a power-law distribution, where small events are common, and large events are rare but possible.

2. Threshold-Based Behavior: In SOC systems, elements accumulate energy or stress until they reach a threshold, at which point they release energy, affecting neighboring elements and possibly triggering chain reactions.

3. Slow-Driving and Fast-Relaxation: SOC systems typically evolve slowly as energy or stress accumulates gradually. When a critical point is reached, the system undergoes a rapid "relaxation" or redistribution of energy, producing events of various sizes.

Examples of Self-Organized Criticality

SOC systems are found across nature and often exhibit behaviors seen in phenomena such as:

Earthquakes: Stress builds up in tectonic plates until a fault "slips" and releases the stress, sometimes causing cascading earthquakes or aftershocks.

Sandpiles: A classic example used to describe SOC. As grains of sand are slowly added to a pile, they occasionally trigger avalanches, with the size of each avalanche varying widely and following a power-law distribution.

Forest Fires: In forests, trees accumulate fuel over time. When a fire starts, it can burn a few trees or spread widely, depending on local conditions, like tree density.

Neural Networks: In the brain, neuronal activity exhibits avalanches in which clusters of neurons fire together in patterns that are scale-invariant, suggesting the brain may operate near a critical point for optimal information processing.

Mathematical Modeling and Theory

Mathematically, SOC systems are often studied through cellular automata, sandpile models, and percolation theory, which capture how local interactions can produce global criticality. SOC systems display a type of fractal structure in space or time, where similar patterns can be observed on different scales.

Why SOC is Important

Self-organized criticality provides a framework for understanding how complex systems can operate at the edge of chaos, where small changes have the potential to trigger massive, system-wide effects. SOC is especially valuable in understanding natural systems that are not directly controlled or tuned but still exhibit organized, critical behavior without external direction. This concept also gives insights into optimizing systems for adaptability, robustness, and efficient response to stimuli in fields ranging from biology to economics and even computer science.

The study of SOC systems has reshaped our understanding of how patterns and complexity emerge in nature, showing how local interactions alone can drive systems to reach a delicate balance between order and chaos.

Cyclic universe

The cyclic universe is a concept in cosmology proposing that the universe undergoes endless cycles of expansion and contraction, avoiding a true beginning or end in time. This model suggests that, rather than a single Big Bang and eventual heat death or "Big Rip" as in the standard cosmological model, the universe goes through phases of birth, evolution, collapse, and rebirth, perpetually cycling.

Key Concepts in Cyclic Universe Models

1. Bounce Mechanism: In cyclic models, the universe doesn't collapse into a singularity (as in a "Big Crunch") and stop. Instead, it "bounces" back into an expanding phase, potentially triggered by unknown quantum or gravitational effects that prevent total collapse.

2. Entropy Reset: One of the main challenges for cyclic models is how entropy (disorder) is managed, as cycles of increasing entropy would imply that each cycle becomes progressively less viable. Some models propose that each "bounce" resets the universe's entropy or expands into a vastly larger space, effectively "resetting" conditions.

3. Dark Energy and Dark Matter: In some cyclic theories, dark energy and dark matter play crucial roles in controlling the timing and behavior of each cycle, either accelerating expansion or modulating collapse.

Types of Cyclic Universe Theories

Ekpyrotic Theory: Developed by cosmologists like Paul Steinhardt and Neil Turok, this theory suggests that cyclic events are driven by collisions between parallel "branes" in higher-dimensional space, leading to repeated creation and destruction of universes [5].

Conformal Cyclic Cosmology (CCC): Proposed by Roger Penrose, CCC suggests that the universe’s structure changes with each cycle, but in a way that future infinities and Big Bang singularities become indistinguishable, effectively connecting the end of one cycle to the beginning of another.

Evidence and Challenges

While the cyclic universe is a mathematically compelling idea, there is limited observational evidence to support it, especially given the lack of a clear mechanism for a "bounce" and entropy reset. Cosmic microwave background (CMB) radiation and large-scale structures provide some hints, but definitive observational proof remains elusive.

The cyclic universe is part of a broader category of "alternative cosmologies" that seek to address some of the unanswered questions in standard Big Bang cosmology, especially regarding the beginning and fate of the universe.

The widely accepted Big Bang theory describes the universe's origin as a singular, infinitely dense point that rapidly expanded, marking the beginning of space and time.

Immediately after the Big Bang, the universe underwent a brief but exponential expansion, giving rise to the large-scale structure we observe today. As the universe continues to expand, it cools and the formation of galaxies, stars, and other celestial bodies occurs.

In Cyclic model, the universe expands, driven by the repulsive force of dark energy, leading to the formation of structures like galaxies and galaxy clusters. As the expansion slows due to the gravitational pull of matter, the universe enters a phase of deceleration, preparing for the eventual contraction. Ultimately, the attractive force of gravity overcomes the expansive force of dark energy, causing the universe to begin contracting, setting the stage for the next cycle.

The gravitational influence of dark matter is thought to contribute to the formation of cosmic structures and the eventual contraction of the universe.

Detections of gravitational waves could potentially reveal signatures of previous contractions and expansions.

If the cyclic universe model is correct, the universe may continue to cycle through an endless series of expansions and contractions, with the potential for new forms of life and energy to emerge.

Every Big Bang is the criticality point in the SOC concept. Expansion is an avalanche. After some time with accelerating expansion,the universe is collapsing. The energy input for another Big Bang is accummulating.If the universe is osscilating, the collapses play energy input role.

References

[1] Bak, P., C. Tang, K. Wiesenfeld, Self-organized criticality: an explanation of 1/f noise. Phys.Rev. Letters 59(4): 381-384, doi:10.1103/PhysRevLett. 59.381,1987

[2] Aschwanden, M.J., Crosby, N.B., Dimitropoulou, M., Georgoulis, M.K., Hergarten, S., McAteer, J., Milovanov, A.V., Mineshige, S., Morales, L., Nishizuka, N., Pruessner, G., Sanchez, R., Sharma, A.S., Strugarek, A., Uritsky, V., 25 years of self-organized criticality: Solar and astrophysics. Space Sci. Rev. 198, 47. doi 10.1007/s11207-016-0910-5, 2016

[3] Marek, M., and R. Schreiber, Is the AKR Cyclotron Maser Instability a self-organized criticality system? In Planetary Radio Emissions VIII, edited by G. Fischer, G. Mann, M. Panchenko, and P. Zarka, Austrian Academy of Sciences Press, Vienna, 269 -277, 2017

[4] Marek, M., and R. Schreiber, Can the Auroral Kilometric Radiation be a Self- Organized Criticality System? Earth and Space Science, Volume 9, Issue 5, article id. E02148, doi 10.1029/2021EA002148 , 2022

[5] Steinhardt, P.J., Turok, N., Endless Universe: Beyond the Big Bang, ISBN-10:0385509642, 2007