Chaotic Universe Model: “Our universe consists of much more than just perceivable matter”

“The standard model is essentially incorrect” - Theoretical physicist Ekrem Aydiner, Istanbul University Physics Department

Scientific Reports volume 8, Article number: 721 (2018) |

Abstract
In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for (...) values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.

Introduction
The formation, structure, dynamics and evolution of the universe has always been of interest. It is commonly accepted that modern cosmology began with the publication of Einstein’s seminal article in 19171. Applying the general relativity to the entire universe, Einstein suggested that the universe was static, and spatially curved. Following from this, to explain the structure and dynamics of the universe many interesting models based on Einstein model have been proposed such as flat and expanding universe2, expanding flat space model, spherical and hyperbolic expanding space3, original big-bang model, expanding flat space, kinematic expanding models8, oscillating or cyclic universe models, buble universe and inflation bubble universe models, chaotic inflation model etc. Amongst these models, the big-bang model has been the most accepted one. This is due to the cosmic microwave background (CMB), and cosmic red shift discovered by Hubble observations as well as observations confirming the abundance of light elements in the universe supporting the big-bang scenario. However, new experimental findings such as Type Ia supernovae (SNIa) data, CMB anisotropy, and large scale structure (LSS), showing that the universe does not only expand but does this with an acceleration makes this cosmic scenario more exciting. There is no explanation to this expansion with an acceleration yet. Cosmologists are still working on new models and scenarios to address this situation. One of the best scenarios attempting this is the dark energy. Unfortunately, there is no confirmation of the physical source of this dark energy. Although the origin of the dark energy is not known yet, it is well known that mater is not the only ingredient of the universe. According to what is known today, at present, the universe is composed of approximately 75% dark energy, 20% cold dark matter, 5% baryonic matter and negligible amount of radiation. To explain the nature of the dark energy, there are various dark energy models and mechanisms such as the cosmological constant Λ (vacuum or dark energy) proposed. The cosmological constant-cold dark matter-matter model (CDM) works very well and is in agreement with a large number of recent observations. However, to state without considering highly hypothetical models and their problematic propositions, some of the questions to be answered are the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, emergence of the galaxies, matter distribution and large scale organization of the universe. Despite the great success of the modern cosmology, it is obvious that there can be no success in the development of an integrated theory on the dynamics and evolution of the universe without answering these questions.

There are many proposed models attempting to answer questions above mentioned emerge from the big-bang and other theories based on the theory of the modern cosmology founded by Einstein. For example, oscillating or cyclic universe models, and dark-matter interaction model were proposed to solve the singularity, and fine tuning problems respectively gaining importance in the field. However, no theoretical relationship has been established between the cyclic universe and the dark energy-dark matter interaction models so far, sufficiently addressing the evolution and dynamics of the universe. Questions on the past and future evolution of the universe, and the mechanisms of the dynamics stemming from this evolution have not sufficiently been addressed. But until now, a more comprehensive scenario has not been developed that addresses the evolution of the universe and the existing cosmological problems. Work based on the interaction of dark energy and dark matter seems to bring optimism to the field. This is because the presence of such interactions may have hints that may help to understand the dynamics of the universe leading to a the development of a more realistic scenario. In this work, in contrast to well known popular models, it is assumed that there is a non-linear interaction between dark energy, dark matter, matter and radiation. Although somehow hypothetical, this assumption may have the potential of solving many important problems of cosmology such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, emergence of galaxies, matter distribution and large scale organization of the universe.

The idea of presence of a non-linear interaction between dark energy, dark matter, matter and radiation may enable the development of a new cosmology scenario on the evolution and dynamics of the universe. In this work, the interactions between components forming the universe is modeled and possible outcomes are discussed. This model is a novel one. The interaction models are based on Friedman-Robertson-Walker (FRW) framework leading to investigation of possible dynamics. We believe in the importance of this work because of the following points: Firstly, the non-linear interaction between the components of the universe were first given by the Lotka-Volterra type equations49,50. It is known that the Lotka-Volterra equation and its variations are mathematical models proposed to model the competition between biological species. It is interesting that the Lotka-Volterra type equation written for cosmology is in the simplest differential form. Secondly, the Lotka-Volterra type equations written for cosmology can give chaotic solutions depending on the values of the parameters of interaction. This is an important outcome for cosmology carrying a potential in helping us to understand questions mentioned above using the non-linear interaction dynamic. Furthermore, the model proposed here combines the big-bang and oscillating universe models in a different way and a perspective.

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