Thermodynamics of the universe
Encyclopedia
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 analytically.
, one can approximate its thermodynamics
by neglecting interactions between particles, and assuming all the energy
is in the form of heat
. Then by the first law of thermodynamics
:
Where
is the total heat which is assumed to be constant, 
is the internal energy of the matter and radiation in the universe, 
is the pressure and 
the volume.
One then finds an equation for the energy density
, and so
where in the last equality we used the fact that the total volume of the universe is proportional to
, 
being the scale factor
of the universe.
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
and identifying 
(the energy density), we get one of the FLRW equations of motions.
In the comoving coordinates,
is equal to the mass density 
. For radiation, 
whereas for matter 
and the pressure can be neglected. Thus we get:
For radiation
thus
is proportional to 
For matter
thus
is proportional to 
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
.
For radiation
, the energy density
depends on the temperature
as well, and is therefore proportional to 
. As the universe expands it cools down, so 
depends on 
as well. In fact, since the energy
of a relativistic particle
is inversely proportional to its wavelength
, which is proportional to
, the energy density
of the radiation
must be proportional to
.
From this discussion it is also obvious that the temperature
of radiation is inversely proportional to the scale factor
.
and the curvatue parameter 
, which is justified for the early universe (
), one gets the following equation:
is the energy density, and one finds the following behavior:
One can further show that the universe was radiation-dominated as long as the energy density
was of the order of 10 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 became matter dominant.
In the universe today, matter is mainly in forms of 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
.
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 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.
According to the equation above,
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.
In fact, if the dark energy
is created by a cosmological constant
or a constant scalar field
, then its pressure is minus its energy density
, and therefore its energy density remains constant (as is expected by definition).
Dark energy
is usually assumed to be the Casimir energy of the vacuum, with possible contributions from the energy density of scalar field
s which has a non-zero 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.
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.
Relativistic particle
A relativistic particle is a particle which moves with a relativistic speed; that is, a speed comparable to the speed of light. This is achieved by photons to the extent that effects described by special relativity are able to describe those of such particles themselves...
s which are referred to as radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
, 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
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
is much lower than their rest mass and therefore move much slower than the speed of light. The intermediate case is not treated well analytically.
Energy density in the expanding universe
If the universe is not undergoing a phase transitionPhase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
, one can approximate its thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
by neglecting interactions between particles, and assuming all the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
is in the form of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
. Then by the first law of thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...
:
Where
is the total heat which is assumed to be constant, is the internal energy of the matter and radiation in the universe, is the pressure and the volume.One then finds an equation for the energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
, and sowhere in the last equality we used the fact that the total volume of the universe is proportional to
, being the scale factorScale factor (Universe)
The scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor...
of the universe.
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
and identifying (the energy density), we get one of the FLRW equations of motions.In the comoving coordinates,
is equal to the mass density . For radiation, whereas for matter and the pressure can be neglected. Thus we get:For radiation
thus
is proportional to For matter
thus
is proportional to This can be understood as follows: For matter, the energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
is equal (in our approximation) to the rest mass density. This is inversely proportional to the volume, and is therefore proportional to
.For radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
, the energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
depends on the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
as well, and is therefore proportional to . As the universe expands it cools down, so depends on as well. In fact, since the energyEnergy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
of a relativistic particle
Relativistic particle
A relativistic particle is a particle which moves with a relativistic speed; that is, a speed comparable to the speed of light. This is achieved by photons to the extent that effects described by special relativity are able to describe those of such particles themselves...
is inversely proportional to its wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
, which is proportional to
, the energy densityEnergy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
of the radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
must be proportional to
.From this discussion it is also obvious that the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
of radiation is inversely proportional to the scale factor
Scale factor (Universe)
The scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor...
.Rate of expansion of the universe
Plugging this information to the Friedmann-Lemaître-Robertson-Walker equations of motion and neglecting both the cosmological constantCosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
and the curvatue parameter , which is justified for the early universe (), one gets the following equation: is the energy density, and one finds the following behavior:
- In a radiation-dominated universe
- In a matter-dominated universe
One can further show that the universe was radiation-dominated as long as the energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
was of the order of 10 eV
Electronvolt
In physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...
to the fourth, or higher. Since the energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
keeps going down, this was no longer true when the universe was 70,000 years old, when it became matter dominant.
In the universe today, matter is mainly in forms of galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
and dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
, while the radiation is the cosmic microwave background radiation
Cosmic microwave background radiation
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....
, the cosmic neutrino background
Cosmic neutrino background
The cosmic neutrino background is the universe's background particle radiation composed of neutrinos.Like the cosmic microwave background radiation , the CνB is a relic of the big bang, and while the CMB dates from when the universe was 379,000 years old, the CνB decoupled from matter when the...
(if the neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
rest mass is high enough then the latter is formally matter), and finally, mostly in the form of dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
.
Dark energy and cosmic inflation
Dark energyDark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
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 negative pressure
Negative pressure
Negative pressure may refer to:*negative pressure as opposed to positive pressure*stretched liquid*vacuum*negative gauge pressure, a way of expressing pressure measurements below atmospheric pressure*suction*transpirational pull...
: in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
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
Negative pressure
Negative pressure may refer to:*negative pressure as opposed to positive pressure*stretched liquid*vacuum*negative gauge pressure, a way of expressing pressure measurements below atmospheric pressure*suction*transpirational pull...
causes gravitational repulsion and thus accelerates the expansion of the universe.
According to the equation above,
Thus the more negative the pressure is, the less the energy density reduces as the universe expands. In other words, Dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
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.
In fact, if the dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
is created by a cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
or a constant scalar field
Scalar field theory
In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a "scalar", in contrast to a vector or tensor field...
, then its pressure is minus its energy density
, and therefore its energy density remains constant (as is expected by definition).Dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
is usually assumed to be the Casimir energy of the vacuum, with possible contributions from the energy density of scalar field
Scalar field theory
In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a "scalar", in contrast to a vector or tensor field...
s which has a non-zero value
Vacuum expectation value
In quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...
at the vacuum. It may be that this field can decay at some time in the distant future, leading to a new vacuum state
Vacuum state
In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...
, different than the one we are living in. This is a phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
, where the dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
is reduced and huge amounts of energy in conventional forms (i.e. particles) are produced.
Such a series of events is in fact thought to have already occurred in the early universe, where first a cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
much larger than the present one came to dominate the universe, bringing about cosmic inflation
Cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...
. At the end of this epoch, a phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
occurred where the cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
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.
See also
- Physical cosmologyPhysical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...
- Friedmann-Lemaître-Robertson-Walker metric
- Dark energyDark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
- Cosmic inflationCosmic inflationIn physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...
- ThermodynamicsThermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
- First law of thermodynamicsFirst law of thermodynamicsThe first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...