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| The '''thermodynamics of the universe''' is dictated by which form of energy dominates it - [[relativistic particle]]s which are referred to as [[radiation]], or non-relativistic particles which are referred to as matter. The former are particles whose [[rest mass]] is zero or negligible compared to their energy, and therefore move at the speed of light or very close to it; the latter are particles whose [[kinetic energy]] is much lower than their [[rest mass]] and therefore move much slower than the speed of light. The intermediate case is not treated well [[analytic solution|analytically]].
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| ==Energy density in the expanding universe==
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| If the universe is expanding adiabatically then it will satisfy the [[first law of thermodynamics]]:
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| <math>0 = dQ = dU + P dV</math>
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| where <math>Q</math> is the total heat which is assumed to be constant, <math>U</math> is the internal energy of the matter and radiation in the universe, <math>P</math> is the pressure and <math>V</math> the volume.
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| One then finds an equation for the [[energy density]] <math>u\equiv U/V</math>, and so
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| <math>du = d\left({U\over V}\right)={dU\over V}-U{dV\over V^2}=-(p+u){dV\over V} = -3(p+u){da\over a}</math>
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| where in the last equality we used the fact that the total volume of the universe is proportional to <math>a^3</math>, <math>a</math> being the [[Scale factor (Universe)|scale factor]] of the universe.
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| In fact this equation can be directly obtained from the equations of motion governing the [[Friedmann-Lemaître-Robertson-Walker metric]]: by dividing the equation above with <math>dt</math> and identifying <math>\rho = u</math> (the energy density), we get one of the [[Friedmann-Lemaître-Robertson-Walker metric#Interpretation|FLRW equations of motions]].
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| In the [[comoving coordinates]], <math>u</math> is equal to the [[mass density]] <math>\rho</math>. For radiation, <math>p=u/3</math> whereas for matter <math>p<<u</math> and the pressure can be neglected. Thus we get:
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| For radiation
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| <math>du = -4u {da\over a}</math>
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| thus <math>u</math> is proportional to <math>a^{-4}</math>
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| For matter
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| <math>du = -3u {da\over a}</math>
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| thus <math>u</math> is proportional to <math>a^{-3}</math>
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| This can be understood as follows: For matter, the [[energy density]] is equal (in our approximation) to the [[rest mass]] density. This is inversely proportional to the volume, and is therefore proportional to <math>a^{-3}</math>.
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| For [[radiation]], the [[energy density]] depends on the [[temperature]] <math>T</math> as well, and is therefore proportional to <math>T a^{-3}</math>. As the universe expands it cools down, so <math>T</math> depends on <math>a</math> as well. In fact, since the [[energy]] of a [[relativistic particle]] is inversely proportional to its [[wavelength]], which is proportional to <math>a</math>, the [[energy density]] of the [[radiation]] must be proportional to <math>a^{-4}</math>.
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| From this discussion it is also obvious that the [[temperature]] of radiation is inversely proportional to the [[Scale factor (Universe)|scale factor]] <math>a</math>.
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| ==Rate of expansion of the universe==
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| Plugging this information to the [[Friedmann-Lemaître-Robertson-Walker metric|Friedmann-Lemaître-Robertson-Walker]] [[equations of motion]] and neglecting both the [[cosmological constant]] <math>\Lambda</math> and the curvatue parameter <math>k</math>, which is justified for the early universe (<math>a\ll 1</math>), one gets the following equation:
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| :<math> {{\dot a}^2} \propto {a^2} \rho</math></center>
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| <math>\rho = u</math> is the energy density, and one finds the following behavior:
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| * In a radiation-dominated universe: <math>a \propto t^{1/2}</math>
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| * In a matter-dominated universe: <math>a \propto t^{2/3}</math>
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| One can further show that the universe was radiation-dominated as long as the [[energy density]] was of the order of 10 [[Electronvolt|eV]] to the fourth, or higher. Since the [[energy density]] keeps going down, this was no longer true when the universe was 70,000 years old, when it [[Cosmological timeline#Matter domination: 70,000 years|became matter dominant]].
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| In the universe today, matter is mainly in forms of [[galaxy|galaxies]] and [[dark matter]], while the radiation is the [[cosmic microwave background radiation]], the [[cosmic neutrino background]] (if the [[neutrino]] [[rest mass]] is high enough then the latter is formally matter), and finally, mostly in the form of [[dark energy]].
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| ==Dark energy and cosmic inflation==
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| [[Dark energy]] is a hypothetical form of energy that permeates all of space, and causes an acceleration in the expansion of the universe due to its strong [[Pressure#Negative pressures|negative pressure]]: in [[general relativity]], [[pressure]] has a gravitational effect similar to that of energy and mass, and while positive pressure causes gravitational attraction and thus decelerates the expansion of the universe, negative pressure causes gravitational repulsion and thus accelerates the expansion of the universe.
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| According to the equation above,
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| :<math>{\dot u} = -3(p+u)\frac{\dot a}{a}</math>
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| Thus the more negative the pressure is, the less the energy density reduces as the universe expands. In other words, [[Dark energy]] dilutes less than any other form of energy, and will therefore eventually dominate the universe, as all other energy densities gets diluted faster with the expansion of the universe.
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| In fact, if the [[dark energy]] is created by a [[cosmological constant]] or a constant [[Scalar field theory|scalar field]], then its pressure is minus its energy density <math>p = -u</math>, and therefore its energy density remains constant (as is expected by definition).
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| [[Dark energy]] is usually assumed to be the [[Casimir energy]] of the [[Vacuum#Quantum-mechanical definition|vacuum]], with possible contributions from the energy density of [[Scalar field theory|scalar field]]s which has a non-zero [[Vacuum expectation value|value]] at the vacuum. It may be that this field can decay at some time in the distant future, leading to a new [[vacuum state]], different than the one we are living in. This is a [[phase transition]], where the [[dark energy]] is reduced and huge amounts of energy in conventional forms (i.e. particles) are produced.
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| Such a series of events is in fact thought to have already occurred in the early universe, where first a [[cosmological constant]] much larger than the present one came to dominate the universe, bringing about [[cosmic inflation]]. At the end of this epoch, a [[phase transition]] occurred where the [[cosmological constant]] was reduced to its present value and huge amounts of energy where produced, from which all the radiation and matter of the early universe came about.
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| ==See also==
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| *[[Physical cosmology]]
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| *[[Friedmann-Lemaître-Robertson-Walker metric]]
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| *[[Dark energy]]
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| *[[Cosmic inflation]]
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| *[[Thermodynamics]]
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| *[[First law of thermodynamics]]
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| [[Category:Physical cosmology]]
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Hello and welcome. My title is Ling. Arizona has usually been my living location but my spouse desires us to move. His day occupation is a cashier and his salary has been truly satisfying. Climbing is what love performing.
Also visit my webpage :: http://praxis-simone-ernstberger.de/index.php?mod=users&action=view&id=8591