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Information about Equation Of State (cosmology)

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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 ρ: . It is closely related to the thermodynamic equation of state and ideal gas law.[1] The equation of state may be used in Friedmann-Lemaître-Robertson-Walker equations to describe the evolution of an isotropic universe filled with a perfect fluid. If a is the scale factor then
If the fluid is the dominant form of matter in a flat universe, then
where is the proper time.

In general the Friedmann acceleration equation is
where is the cosmological constant and is Newton's constant, and is the second proper time derivative of the scale factor.

If we define (what might be called "effective") energy density and pressure as
and
the acceleration equation may be written as


The equation of state of ordinary non-relativistic matter (e.g. cold dust) is , which means that it is diluted as , where is the volume. This means that the energy density red-shifts as the volume, which is natural for ordinary non-relativistic matter. The equation of state of ultra-relativistic matter (e.g. radiation, but also matter in the very early universe) is which means that it is diluted as . In an expanding universe, the energy density decreases more quickly than the volume expansion, because radiation has momentum and, by the de Broglie hypothesis a wavelength, which is red-shifted.

Cosmic inflation and the accelerated expansion of the universe can be characterized by the equation of state of dark energy. In the simplest case, the equation of state of the cosmological constant is . In this case, the above expression for the scale factor is not valid and , where the constant H is the Hubble parameter. More generally, the expansion of the universe is accelerating for any equation of state . Phantom energy has equation of state , and causes a Big Rip.

In an expanding universe, fluids with larger equations of state disappear more quickly than those with smaller equations of state. This is the origin of the flatness and monopole problems of the big bang: curvature has and monopoles have , so if they were around at the time of the early big bang, they should still be visible today. These problems are solved by cosmic inflation which has . Measuring the equation of state of dark energy is one of the largest efforts of observational cosmology. By accurately measuring w, it is hoped that the cosmological constant could be distinguished from quintessence which has .

A scalar field can be viewed as a sort of perfect fluid with equation of state
where is the time-derivative of and is the potential energy. A free () scalar field has , and one with vanishing kinetic energy is equivalent to a cosmological constant: . Any equation of state in between is achievable, which makes scalar fields useful models for many phenomena in cosmology.

Notes

1. ^ The perfect gas equation of state may be written as
where is the mass density, R is the particular gas constant, T is the temperature and C = (RT)1/2 is a characteristic thermal speed of the molecules. Thus
where and for a "cold" gas.
Physical cosmology, as a branch of astronomy, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause.
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The age of the universe, in physics, is the time elapsed between the Big Bang and the present day. Current observations suggest that this is about 13.7 billion years, with an uncertainty of about +/-200 million years.
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Big Bang is the cosmological model of the universe whose primary assertion is that the universe has expanded into its current state from a primordial condition of enormous density and temperature.
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Blue Shift refers to a shortening of a transmitted signal's wavelength, and/or an increase in its frequency. The name comes from the fact that the shorter-wavelength end of the optical spectrum is the blue (or violet) end, hence, when visible light is compacted in
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In standard cosmology, 'comoving' distance or 'proper distance' is one of several distance measures used by cosmologists to define distances between objects.

Comoving coordinates


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cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR, also referred to as relic radiation) is a form of electromagnetic radiation discovered in 1965 that fills the entire universe [1].
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In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. [1]
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In astrophysics and cosmology, dark matter is hypothetical matter of unknown composition that does not emit or reflect enough electromagnetic radiation to be observed directly, but whose presence can be inferred from gravitational effects on visible matter.
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Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of the Einstein field equations of general relativity; it describes a , isotropic expanding or contracting universe.
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The Friedmann equations are a set of equations in cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity.
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formation of galaxies is still one of the most active research areas in astrophysics; and, to some extent, this is also true for galaxy evolution. Some ideas, however, have gained wide acceptance.
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Hubble's law is a statement in physical cosmology which states that the redshift in light coming from distant galaxies is proportional to their distance. The law was first formulated by Edwin Hubble and Milton Humason in 1929[1] after nearly a decade of observations.
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In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density.
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large-scale structure refers to the characterization of observable distributions of matter and light on the largest scales (typically on the order of billions of light-years).
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ΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. It is frequently referred to as the concordance model of big bang cosmology, since it attempts to explain cosmic microwave background observations, as well as large scale structure
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The metric expansion of space is a key part of science's current understanding of the universe, whereby spacetime itself is described by a metric which changes over time in such a way that the spatial dimensions appear to grow or stretch as the universe gets older.
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In physical cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than those of H-1 (i.e. the normal, light isotope of hydrogen, whose nuclei consist of a single proton each) during the early phases of the
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This article or section may contain inappropriate or misinterpreted which do not the text.
Please help [ improve this article] by checking for inaccuracies. This article has been tagged since October 2007.
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redshift occurs when the electromagnetic radiation, usually visible light, that is emitted from or reflected off an object is shifted toward the (less energetic) red end of the electromagnetic spectrum.
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The shape of the Universe is an informal name for a subject of investigation within physical cosmology. Cosmologists and astronomers describe the geometry of the universe which includes both local geometry and global geometry.
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Structure formation refers to a fundamental problem in physical cosmology. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.7 Gyr ago.
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Physical cosmology

  • Age of the universe
  • Big Bang
  • Blueshift
  • Comoving distance
  • Cosmic microwave background
  • Dark energy
  • Dark matter
  • FLRW metric
  • Friedmann equations
  • Galaxy formation
  • Hubble's law
  • Inflation

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For a timeline of the cosmos (or universe), see .


This timeline of cosmological theories and discoveries is a chronological catalog of the evolution of humankind's understanding of the cosmos over the last two-plus millennia.
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The ultimate fate of the universe is a topic in physical cosmology. Many possible fates are predicted by rival scientific theories, including futures of both finite and infinite duration.
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The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. Based on observations of the portion of the Universe that is observable, physicists attempt to describe the whole of space-time, including all matter and
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Astronomy is the scientific study of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation).
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General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16.[1] It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational
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Particle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. It is also called "high energy physics"
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Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity.
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Physical cosmology, as a branch of astronomy, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause.
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