In

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

,

**quintessence** is a

hypotheticalA hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

form of

dark 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...

postulated as an explanation of observations of an

accelerating universeThe accelerating universe is the observation that the universe appears to be expanding at an increasing rate, which in formal terms means that the cosmic scale factor a has a positive second derivative, implying that the velocity at which a given galaxy is receding from us should be continually...

. It has been proposed by some physicists to be a

fifth fundamental forceOccasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. The force is generally believed to have roughly the strength of gravity Occasionally, physicists have postulated the existence of a fifth force in addition to the four known...

. Quintessence differs from the

cosmological constantIn 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...

explanation of dark energy in that it is a dynamic equation that changes over time, unlike the cosmological constant which always stays constant throughout history from beginning to end. It is suggested that quintessence can be either attractive or repulsive depending on the ratio of kinetic to potential energy in the universe. Specifically, it is thought that quintessence became repulsive about 10 billion years ago (the universe is approximately 14 billion years old).

## Scalar field

Quintessence is a

scalar fieldIn mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...

whose

equation of stateIn 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=p/\rho...

*w*_{q}, defined as the ratio of its pressure

*p*_{q} and its density

_{q}, is given by the potential energy

and a kinetic term:

.

Hence, Quintessence is dynamic, and generally has a density and equation of state that varies with time. By contrast, a

Cosmological ConstantIn 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...

is static, with a fixed energy density and

*w*_{q} = −1.

## Tracker behavior

Many models of quintessence have a

*tracker* behavior, which according to

Paul SteinhardtPaul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. He received his B.S. at the California Institute of Technology and his Ph.D. in Physics at Harvard University...

*et al.* (1999) partly solves the cosmological constant problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until

matter-radiation equalityThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

, which triggers quintessence to start having characteristics similar to

dark 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...

, eventually dominating the universe. This naturally sets the low scale of the

dark 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...

. When comparing the predicted

expansion rateThe metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

of the universe as given by the tracker solutions with cosmological data, a main feature of tracker solutions is that one needs four parameters to properly describe the behavior of their

equation of stateIn 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=p/\rho...

, whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data (horizon 2015-2020).

## Specific models

Some special cases of quintessence are

phantom energyPhantom energy is a hypothetical form of dark energy with equation of state \! w Phantom energy is a hypothetical form of dark energy with equation of state...

, in which

*w*_{q} < −1, and k-essence (short for kinetic quintessence), which has a non-standard form of

kinetic energyThe 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...

. If this type of energy were to exist, it would cause a

big ripThe Big Rip is a cosmological hypothesis first published in 2003, about the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, is progressively torn apart by the expansion of the universe at a certain time in the future...

in the universe due to the growing energy density of dark energy which would cause the expansion of the universe to increase at a faster-than-exponential rate.

## Quintom scenario

In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that the equation of state had possibly crossed the cosmological constant boundary (w=-1) from above to below. A proven "No-Go" theorem indicates this situation, called the

Quintom scenarioQuintom scenario is a hypothetical scenario of dark energy with the equation of state crossing the cosmological constant boundary from above to below, or oppositely...

, requires at least two degrees of freedom for dark energy models.

## Terminology

The name comes from the classical elements of the ancient

GreeksThe Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....

. The

aetherAccording to ancient and medieval science aether , also spelled æther or ether, is the material that fills the region of the universe above the terrestrial sphere.-Mythological origins:...

, a pure "fifth element" (

*quinta essentia* in Latin), was thought to fill the Universe beyond Earth. This seemed fitting to modern scientists, since quintessence was the fifth known contribution to the overall mass-energy content of the Universe. (The other four in the modern interpretation, different from the Greeks' ideas, are:

baryonic matterA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...

; radiation – photons and the highly relativistic neutrinos, which may be considered

hot dark matterHot dark matter is a hypothetical form of dark matter which consists of particles that travel with ultrarelativistic velocities. The best candidate for the identity of hot dark matter is the neutrino. Neutrinos have very small masses, and do not take part in two of the four fundamental forces, the...

;

cold dark matterCold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...

; and the term due to spatial curvature – loosely,

gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

al

self-energyIn theoretical physics and quantum field theory a particle's self-energy \Sigma represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and the system it is part of...

.)

In

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

,

**quintessence** is a

hypotheticalA hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

form of

dark 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...

postulated as an explanation of observations of an

accelerating universeThe accelerating universe is the observation that the universe appears to be expanding at an increasing rate, which in formal terms means that the cosmic scale factor a has a positive second derivative, implying that the velocity at which a given galaxy is receding from us should be continually...

. It has been proposed by some physicists to be a

fifth fundamental forceOccasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. The force is generally believed to have roughly the strength of gravity Occasionally, physicists have postulated the existence of a fifth force in addition to the four known...

. Quintessence differs from the

cosmological constantIn 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...

explanation of dark energy in that it is a dynamic equation that changes over time, unlike the cosmological constant which always stays constant throughout history from beginning to end. It is suggested that quintessence can be either attractive or repulsive depending on the ratio of kinetic to potential energy in the universe. Specifically, it is thought that quintessence became repulsive about 10 billion years ago (the universe is approximately 14 billion years old).

## Scalar field

Quintessence is a

scalar fieldIn mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...

whose

equation of stateIn 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=p/\rho...

*w*_{q}, defined as the ratio of its pressure

*p*_{q} and its density

_{q}, is given by the potential energy

and a kinetic term:

.

Hence, Quintessence is dynamic, and generally has a density and equation of state that varies with time. By contrast, a

Cosmological ConstantIn 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...

is static, with a fixed energy density and

*w*_{q} = −1.

## Tracker behavior

Many models of quintessence have a

*tracker* behavior, which according to

Paul SteinhardtPaul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. He received his B.S. at the California Institute of Technology and his Ph.D. in Physics at Harvard University...

*et al.* (1999) partly solves the cosmological constant problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until

matter-radiation equalityThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

, which triggers quintessence to start having characteristics similar to

dark 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...

, eventually dominating the universe. This naturally sets the low scale of the

dark 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...

. When comparing the predicted

expansion rateThe metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

of the universe as given by the tracker solutions with cosmological data, a main feature of tracker solutions is that one needs four parameters to properly describe the behavior of their

equation of stateIn 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=p/\rho...

, whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data (horizon 2015-2020).

## Specific models

Some special cases of quintessence are

phantom energyPhantom energy is a hypothetical form of dark energy with equation of state \! w Phantom energy is a hypothetical form of dark energy with equation of state...

, in which

*w*_{q} < −1, and k-essence (short for kinetic quintessence), which has a non-standard form of

kinetic energyThe 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...

. If this type of energy were to exist, it would cause a

big ripThe Big Rip is a cosmological hypothesis first published in 2003, about the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, is progressively torn apart by the expansion of the universe at a certain time in the future...

in the universe due to the growing energy density of dark energy which would cause the expansion of the universe to increase at a faster-than-exponential rate.

## Quintom scenario

In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that the equation of state had possibly crossed the cosmological constant boundary (w=-1) from above to below. A proven "No-Go" theorem indicates this situation, called the

Quintom scenarioQuintom scenario is a hypothetical scenario of dark energy with the equation of state crossing the cosmological constant boundary from above to below, or oppositely...

, requires at least two degrees of freedom for dark energy models.

## Terminology

The name comes from the classical elements of the ancient

GreeksThe Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....

. The

aetherAccording to ancient and medieval science aether , also spelled æther or ether, is the material that fills the region of the universe above the terrestrial sphere.-Mythological origins:...

, a pure "fifth element" (

*quinta essentia* in Latin), was thought to fill the Universe beyond Earth. This seemed fitting to modern scientists, since quintessence was the fifth known contribution to the overall mass-energy content of the Universe. (The other four in the modern interpretation, different from the Greeks' ideas, are:

baryonic matterA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...

; radiation – photons and the highly relativistic neutrinos, which may be considered

hot dark matterHot dark matter is a hypothetical form of dark matter which consists of particles that travel with ultrarelativistic velocities. The best candidate for the identity of hot dark matter is the neutrino. Neutrinos have very small masses, and do not take part in two of the four fundamental forces, the...

;

cold dark matterCold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...

; and the term due to spatial curvature – loosely,

gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

al

self-energyIn theoretical physics and quantum field theory a particle's self-energy \Sigma represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and the system it is part of...

.)

In

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

,

**quintessence** is a

hypotheticalA hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

form of

dark 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...

postulated as an explanation of observations of an

accelerating universeThe accelerating universe is the observation that the universe appears to be expanding at an increasing rate, which in formal terms means that the cosmic scale factor a has a positive second derivative, implying that the velocity at which a given galaxy is receding from us should be continually...

. It has been proposed by some physicists to be a

fifth fundamental forceOccasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. The force is generally believed to have roughly the strength of gravity Occasionally, physicists have postulated the existence of a fifth force in addition to the four known...

. Quintessence differs from the

cosmological constantIn 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...

explanation of dark energy in that it is a dynamic equation that changes over time, unlike the cosmological constant which always stays constant throughout history from beginning to end. It is suggested that quintessence can be either attractive or repulsive depending on the ratio of kinetic to potential energy in the universe. Specifically, it is thought that quintessence became repulsive about 10 billion years ago (the universe is approximately 14 billion years old).

## Scalar field

Quintessence is a

scalar fieldIn mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...

whose

equation of stateIn 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=p/\rho...

*w*_{q}, defined as the ratio of its pressure

*p*_{q} and its density

_{q}, is given by the potential energy

and a kinetic term:

.

Hence, Quintessence is dynamic, and generally has a density and equation of state that varies with time. By contrast, a

Cosmological ConstantIn 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...

is static, with a fixed energy density and

*w*_{q} = −1.

## Tracker behavior

Many models of quintessence have a

*tracker* behavior, which according to

Paul SteinhardtPaul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. He received his B.S. at the California Institute of Technology and his Ph.D. in Physics at Harvard University...

*et al.* (1999) partly solves the cosmological constant problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until

matter-radiation equalityThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

, which triggers quintessence to start having characteristics similar to

dark 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...

, eventually dominating the universe. This naturally sets the low scale of the

dark 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...

. When comparing the predicted

expansion rateThe metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

of the universe as given by the tracker solutions with cosmological data, a main feature of tracker solutions is that one needs four parameters to properly describe the behavior of their

equation of stateIn 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=p/\rho...

, whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data (horizon 2015-2020).

## Specific models

Some special cases of quintessence are

phantom energyPhantom energy is a hypothetical form of dark energy with equation of state \! w Phantom energy is a hypothetical form of dark energy with equation of state...

, in which

*w*_{q} < −1, and k-essence (short for kinetic quintessence), which has a non-standard form of

kinetic energyThe 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...

. If this type of energy were to exist, it would cause a

big ripThe Big Rip is a cosmological hypothesis first published in 2003, about the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, is progressively torn apart by the expansion of the universe at a certain time in the future...

in the universe due to the growing energy density of dark energy which would cause the expansion of the universe to increase at a faster-than-exponential rate.

## Quintom scenario

In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that the equation of state had possibly crossed the cosmological constant boundary (w=-1) from above to below. A proven "No-Go" theorem indicates this situation, called the

Quintom scenarioQuintom scenario is a hypothetical scenario of dark energy with the equation of state crossing the cosmological constant boundary from above to below, or oppositely...

, requires at least two degrees of freedom for dark energy models.

## Terminology

The name comes from the classical elements of the ancient

GreeksThe Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....

. The

aetherAccording to ancient and medieval science aether , also spelled æther or ether, is the material that fills the region of the universe above the terrestrial sphere.-Mythological origins:...

, a pure "fifth element" (

*quinta essentia* in Latin), was thought to fill the Universe beyond Earth. This seemed fitting to modern scientists, since quintessence was the fifth known contribution to the overall mass-energy content of the Universe. (The other four in the modern interpretation, different from the Greeks' ideas, are:

baryonic matterA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...

; radiation – photons and the highly relativistic neutrinos, which may be considered

hot dark matterHot dark matter is a hypothetical form of dark matter which consists of particles that travel with ultrarelativistic velocities. The best candidate for the identity of hot dark matter is the neutrino. Neutrinos have very small masses, and do not take part in two of the four fundamental forces, the...

;

cold dark matterCold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...

; and the term due to spatial curvature – loosely,

gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

al

self-energyIn theoretical physics and quantum field theory a particle's self-energy \Sigma represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and the system it is part of...

.)