In physical cosmology, fractal cosmology is a set of minority cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is a fractal across a wide range of scales (see also: multifractal system). More generally, it relates to the usage or appearance of fractals in the study of the universe and matter. A central issue in this field is the fractal dimension of the universe or of matter distribution within it, when measured at very large or very small scales. [1]
The first attempt to model the distribution of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987, [2] and a more detailed view of the universe's large-scale structure emerged over the following decade, as the number of cataloged galaxies grew larger. Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a fractal dimension of about 2. [3] The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3.
The universe has been observed to be homogeneous and isotropic (i.e. is smoothly distributed) at very large scales, as is expected in a standard Big Bang or Friedmann-Lemaître-Robertson-Walker cosmology, and in most interpretations of the Lambda-Cold Dark Matter model. The scientific consensus interpretation is that the Sloan Digital Sky Survey (SDSS) suggests that things do indeed smooth out above 100 Megaparsecs.
One study of the SDSS data in 2004 found "The power spectrum is not well-characterized by a single power law but unambiguously shows curvature ... thereby driving yet another nail into the coffin of the fractal universe hypothesis and any other models predicting a power-law power spectrum". [4] Another analysis of luminous red galaxies (LRGs) in the SDSS data calculated the fractal dimension of galaxy distribution (on a scales from 70 to 100 Mpc/h) at 3, consistent with homogeneity, but that the fractal dimension is 2 "out to roughly 20 h−1 Mpc". [5] In 2012, Scrimgeour et al. definitively showed that large-scale structure of galaxies was homogeneous beyond a scale around 70 Mpc/h. [6]
In the realm of theory, the first appearance of fractals in cosmology was likely with Andrei Linde's "Eternally Existing Self-Reproducing Chaotic Inflationary Universe" [7] theory (see chaotic inflation theory) in 1986. In this theory, the evolution of a scalar field creates peaks that become nucleation points that cause inflating patches of space to develop into "bubble universes," making the universe fractal on the very largest scales. Alan Guth's 2007 paper on "Eternal Inflation and its implications" [8] shows that this variety of inflationary universe theory is still being seriously considered today. Inflation, in some form or another, is widely considered to be our best available cosmological model.
Since 1986, quite a large number of different cosmological theories exhibiting fractal properties have been proposed. While Linde's theory shows fractality at scales likely larger than the observable universe, theories like causal dynamical triangulation [9] and the asymptotic safety approach to quantum gravity [10] are fractal at the opposite extreme, in the realm of the ultra-small near the Planck scale. These recent theories of quantum gravity describe a fractal structure for spacetime itself, and suggest that the dimensionality of space evolves with time. Specifically, they suggest that reality is 2D at the Planck scale, and that spacetime gradually becomes 4D at larger scales.
French mathematician Alain Connes has been working for a number of years to reconcile general relativity with quantum mechanics using noncommutative geometry. Fractality also arises in this approach to quantum gravity. An article by Alexander Hellemans in the August 2006 issue of Scientific American [11] quotes Connes as saying that the next important step toward this goal is to "try to understand how space with fractional dimensions couples with gravitation." The work of Connes and physicist Carlo Rovelli [12] suggests that time is an emergent property or arises naturally in this formulation, whereas in causal dynamical triangulation [9] choosing those configurations where adjacent building blocks share the same direction in time is an essential part of the "recipe." Both approaches suggest that the fabric of space itself is fractal, however.
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The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed in 1927 by Roman Catholic priest and physicist Georges Lemaître. Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The overall uniformity of the universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments. However, physics currently lacks a widely accepted theory of quantum gravity that can successfully model the earliest conditions of the Big Bang.
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood.
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch is believed to have lasted from 10−36 seconds to between 10−33 and 10−32 seconds after the Big Bang. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old.
In physical cosmology, the Copernican principle states that humans, on the Earth or in the Solar System, are not privileged observers of the universe, that observations from the Earth are representative of observations from the average position in the universe. Named for Copernican heliocentrism, it is a working assumption that arises from a modified cosmological extension of Copernicus' argument of a moving Earth.
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is uniformly isotropic when viewed on a large enough scale, since the forces are expected to act equally throughout the universe on a large scale, and should, therefore, produce no observable inequalities in the large-scale structuring over the course of evolution of the matter field that was initially laid down by the Big Bang.
The ultimate fate of the universe is a topic in physical cosmology, whose theoretical restrictions allow possible scenarios for the evolution and ultimate fate of the universe to be described and evaluated. Based on available observational evidence, deciding the fate and evolution of the universe has become a valid cosmological question, being beyond the mostly untestable constraints of mythological or theological beliefs. Several possible futures have been predicted by different scientific hypotheses, including that the universe might have existed for a finite and infinite duration, or towards explaining the manner and circumstances of its beginning.
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected. Their existence was first contemplated by the theoretical physicist Tom Kibble in the 1970s.
The Big Bounce hypothesis is a cosmological model for the origin of the known universe. It was originally suggested as a phase of the cyclic model or oscillatory universe interpretation of the Big Bang, where the first cosmological event was the result of the collapse of a previous universe. It receded from serious consideration in the early 1980s after inflation theory emerged as a solution to the horizon problem, which had arisen from advances in observations revealing the large-scale structure of the universe.
Andrei Dmitriyevich Linde is a Russian-American theoretical physicist and the Harald Trap Friis Professor of Physics at Stanford University.
The Lambda-CDM, Lambda cold dark matter or ΛCDM model is a mathematical model of the Big Bang theory with three major components:
Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. Currently, the most widely accepted explanation for their origin is in the context of cosmic inflation. According to the inflationary paradigm, the exponential growth of the scale factor during inflation caused quantum fluctuations of the inflaton field to be stretched to macroscopic scales, and, upon leaving the horizon, to "freeze in". At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the initial conditions for structure formation.
Paul Joseph Steinhardt is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences.
In string theory, the string theory landscape is the collection of possible false vacua, together comprising a collective "landscape" of choices of parameters governing compactifications.
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand, one would like to account for a universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties ; on the other hand, there is the deep question on the origin of the second law of thermodynamics.
Eternal inflation is a hypothetical inflationary universe model, which is itself an outgrowth or extension of the Big Bang theory.
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. Assuming that the lambda-CDM model of cosmology is correct, dark energy is the dominant component of the universe, contributing 68% of the total energy in the present-day observable universe while dark matter and ordinary (baryonic) matter contribute 26% and 5%, respectively, and other components such as neutrinos and photons are nearly negligible. Dark energy's density is very low: 6×10−10 J/m3, much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.
The Huge Large Quasar Group, is a possible structure or pseudo-structure of 73 quasars, referred to as a large quasar group, that measures about 4 billion light-years across. At its discovery, it was identified as the largest and the most massive known structure in the observable universe, though it has been superseded by the Hercules–Corona Borealis Great Wall at 10 billion light-years. There are also issues about its structure.
U1.11 is a large quasar group located in the constellations of Leo and Virgo. It is one of the largest LQG's known, with the estimated maximum diameter of 780 Mpc and contains 38 quasars. It was discovered in 2011 during the course of the Sloan Digital Sky Survey. Until the discovery of the Huge-LQG in November 2012, it was the largest known structure in the universe, beating Clowes–Campusano LQG's 20-year record as largest known structure at the time of its discovery.
The Cosmology Large Angular Scale Surveyor (CLASS) is an array of microwave telescopes at a high-altitude site in the Atacama Desert of Chile as part of the Parque Astronómico de Atacama. The CLASS experiment aims to improve our understanding of cosmic dawn when the first stars turned on, test the theory of cosmic inflation, and distinguish between inflationary models of the very early universe by making precise measurements of the polarization of the Cosmic Microwave Background (CMB) over 65% of the sky at multiple frequencies in the microwave region of the electromagnetic spectrum.