Equation Of State (cosmology)
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Equation Of State (cosmology)
In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number w, equal to the ratio of its pressure p to its energy density \rho: w \equiv \frac. It is closely related to the thermodynamic equation of state and ideal gas law. The equation The perfect gas equation of state may be written as p = \rho_m RT = \rho_m C^2 where \rho_m is the mass density, R is the particular gas constant, T is the temperature and C=\sqrt is a characteristic thermal speed of the molecules. Thus w \equiv \frac = \frac = \frac\approx 0 where c is the speed of light, \rho = \rho_mc^2 and C\ll c for a "cold" gas. FLRW equations and the equation of state The equation of state may be used in Friedmann–Lemaître–Robertson–Walker (FLRW) equations to describe the evolution of an isotropic universe filled with a perfect fluid. If a is the scale factor then \rho \propto a^. If the fluid is the dominant form of matter in a flat universe, then a \propto t^, where t is ...
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Physical Cosmology
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 Cosmogony, origin, structure, Chronology of the universe, evolution, and ultimate fate.For an overview, see Cosmology as a science originated with the Copernican principle, which implies that astronomical object, celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood. Physical cosmology, as it is now understood, began with the development in 1915 of Albert Einstein's general relativity, general theory of relativity, followed by major observational discoveries in the 1920s: first, Edwin Hubble discovered that the universe contains a huge number of external Galaxy, galaxies beyond the Milky Way; then, work by Vesto Sli ...
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Red-shift
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or blueshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. In astronomy and cosmology, the three main causes of electromagnetic redshift are # The radiation travels between objects which are moving apart (" relativistic" redshift, an example of the relativistic Doppler effect) #The radiation travels towards an object in a weaker gravitational potential, i.e. towards an object in less strongly curved (flatter) spacetime (gravitational redshift) #The radiation travels through expanding space (cosmological redshift). The observation that all sufficiently distant light sources show redshift corresponding to their distance from Earth ...
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Scalar Field
In mathematics and physics, a scalar field is a function (mathematics), function associating a single number to every point (geometry), point in a space (mathematics), space – possibly physical space. The scalar may either be a pure Scalar (mathematics), mathematical number (dimensionless) or a scalar (physics), scalar physical quantity (with unit of measurement, units). In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory. Definition Mathematically, a scalar field on a Region (mathematical analysis), region ''U ...
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Quintessence (physics)
In physics, quintessence is a hypothetical form of dark energy, more precisely a scalar field, postulated as an explanation of the observation of an accelerating rate of expansion of the universe. The first example of this scenario was proposed by Ratra and Peebles (1988) and Wetterich (1988). The concept was expanded to more general types of time-varying dark energy, and the term "quintessence" was first introduced in a 1998 paper by Robert R. Caldwell, Rahul Dave and Paul Steinhardt. It has been proposed by some physicists to be a fifth fundamental force. Quintessence differs from the cosmological constant explanation of dark energy in that it is dynamic; that is, it changes over time, unlike the cosmological constant which, by definition, does not change. Quintessence can be either attractive or repulsive depending on the ratio of its kinetic and potential energy. Those working with this postulate believe that quintessence became repulsive about ten billion years ago, a ...
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Observational Cosmology
Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. Early observations The science of physical cosmology as it is practiced today had its subject material defined in the years following the Shapley-Curtis debate when it was determined that the universe had a larger scale than the Milky Way galaxy. This was precipitated by observations that established the size and the dynamics of the cosmos that could be explained by Albert Einstein's General Theory of Relativity. In its infancy, cosmology was a speculative science based on a very limited number of observations and characterized by a dispute between steady state theorists and promoters of Big Bang cosmology. It was not until the 1990s and beyond that the astronomical observations would be able to eliminate competing theories and drive the science to the "Golden Age of Cosmology" which was heralded by ...
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Curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature ''at a point'' of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that is, it is expressed by a single real number. For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surface or man ...
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Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. 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. Crucially, these models are compatible with the Hubble–Lemaître law—the observation that the farther away a galaxy is, the faster it is mo ...
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Monopole Problem
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 lasted from  seconds after the conjectured Big Bang singularity to some time between and  seconds after the singularity. 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 (5.4 billion years ago). Inflation theory was developed in the late 1970s and early 80s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Alexei Starobinsky, Alan Guth, and Andrei Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation." It was developed further in the early ...
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Flatness Problem
The flatness problem (also known as the oldness problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that small deviations from these values would have extreme effects on the appearance of the universe at the current time. In the case of the flatness problem, the parameter which appears fine-tuned is the density of matter and energy in the universe. This value affects the curvature of space-time, with a very specific critical value being required for a flat universe. The current density of the universe is observed to be very close to this critical value. Since any departure of the total density from the critical value would increase rapidly over cosmic time, the early universe must have had a density even closer to the critical density, departing from it by one part in 1062 or less. This leads cosm ...
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Big Rip
In physical cosmology, the Big Rip is a hypothetical cosmological model concerning the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, and even spacetime itself, is progressively torn apart by the expansion of the universe at a certain time in the future, until distances between particles will become infinite. According to the standard model of cosmology, the scale factor of the universe is accelerating, and, in the future era of cosmological constant dominance, will increase exponentially. However, this expansion is similar for every moment of time (hence the exponential law – the expansion of a local volume is the same number of times over the same time interval), and is characterized by an unchanging, small Hubble constant, effectively ignored by any bound material structures. By contrast, in the Big Rip scenario the Hubble constant increases to infinity in a finite time. The possibility of sudden ...
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Phantom Energy
Phantom energy is a hypothetical form of dark energy satisfying the equation of state with w < -1. It possesses negative kinetic energy, and predicts expansion of the universe in excess of that predicted by a , which leads to a . The idea of phantom energy is often dismissed, as it would suggest that the is with

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Hubble Parameter
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum. Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is known as the Hubble flow. It is described by the equation , with ''H''0 the constant of proportionality—the Hubble constant—between the "proper distance" ''D'' to a galaxy, which can change over time, unlike the comoving distance, and its speed of separation ''v'', i.e. the derivative of proper distance with respect to ...
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