Dark energy

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In cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. According to the theory of relativity, the effect of such a negative pressure is qualitatively similar to a force acting in opposition to gravity at large scales. Invoking such an effect is currently the most popular method for explaining the observations of an accelerating universe as well as accounting for a significant portion of the missing mass in the universe.

Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously, and quintessence, a dynamic field whose energy density can vary in time and space. Distinguishing between the alternatives requires high-precision measurements of the expansion of the universe to understand how the speed of the expansion changes over time. The rate of expansion is parameterized by the cosmological equation of state. Measuring the equation of state of dark energy is one of the biggest efforts in observational cosmology today.

Adding a cosmological constant to the standard theory of cosmology (i.e. the FLRW metric) has led to a model for cosmology known as the Lambda-CDM model. This model is in very good agreement with established cosmological observations.

The term dark energy was coined by Michael Turner.


Evidence for dark energy

During the late 1990s, observations of type Ia supernovae suggested that the expansion of the universe is accelerating. These observations have been corroborated by several independent sources since then: the cosmic microwave background, gravitational lensing, age of the universe, big bang nucleosynthesis, large scale structure and measurements of the Hubble parameter, as well as improved measurements of the supernovae. All these elements are consistent with the concordance Lambda-CDM model.

Unsolved problems in physics: Why is the expansion of the universe accelerating, as we have observed? Is our understanding of redshift complete? If it is, then what is the nature of the dark energy driving this acceleration?

The type Ia supernovae provide the most direct evidence for dark energy. Measuring the velocity of receding objects is accomplished easily by measuring the redshift of the receding object. Finding the distance to an object is a more difficult problem, however. It is necessary to find standard candles: objects for which the absolute magnitude is known, so that it is possible to relate the apparent magnitude to the distance. Without standard candles, it is impossible to measure the redshift-distance relation of Hubble's law. Type Ia supernovae are the best known standard candles for cosmological observation, because they are very bright and ignite only when the mass of an old white dwarf star reaches the precisely defined Chandrasekhar limit. The distances to the supernovae are plotted against their velocities, and this is used to measure the expansion history of the universe. These observations indicate that the universe is not decelerating, which would be expected for a matter-dominated universe, but rather is mysteriously accelerating. These observations are explained by postulating a kind of energy with negative pressure (see equation of state (cosmology) for a mathematical explanation): dark energy.

The existence of dark energy, in whatever form, also solves the so-called "missing mass" problem. The theory of big bang nucleosynthesis governs the formation of the light elements in the early universe, such as helium, deuterium and lithium. The theory of large scale structure governs the formation of structure in the universe, stars, quasars, galaxies and galaxy clusters. These theories both suggest that the density of baryons and cold dark matter in the universe is about 30% the critical density for closure of the universe. This is the density necessary to make the shape of the universe flat. Measurements of the cosmic microwave background, most recently by the WMAP satellite, indicate that the universe is very close to flat. Thus, we know that some form of energy must make up the additional 70%.

Nature of dark energy

The exact nature of this dark energy is a matter of speculation. It is known to be very homogeneous, not very dense and doesn't interact strongly through any of the fundamental forces other than gravity. Since it is not very dense—roughly 10−29 grams per cubic centimeter—it is hard to imagine experiments to detect it in the laboratory (but see the references for a claimed detection). Dark energy can only have such a profound impact on the universe, making up 70% of all energy, because it uniformly fills otherwise empty space. The two leading models are quintessence and the cosmological constant.

Cosmological constant

The simplest explanation for dark energy, is that it is simply the "cost of having space": that is, that a volume of space has some intrinsic, fundamental energy. This is the cosmological constant, sometimes called Lambda (hence Lambda-CDM model) after the mathematical symbol used to represent it, the Greek letter Λ. Since energy and mass are related by E = mc2, Einstein's theory of general relativity predicts that it will have a gravitational effect. It is sometimes called a vacuum energy because it is the energy density of empty vacuum. In fact, most theories of particle physics predict vacuum fluctuations that would give the vacuum exactly this sort of energy. The cosmological constant is estimated by cosmologists to be on the order of 10−29g/cm3, or about 10−120 in reduced Planck units.

The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate (see equation of state (cosmology)). The reason why a cosmological constant has negative pressure can be seen from classical thermodynamics. The work done by a change in volume dV is equal to −p dV, where p is the pressure. But the amount of energy in a box of vacuum energy actually increases when the volume increases (dV is positive), because the energy is equal to ρV, where ρ is the energy density of the cosmological constant. Therefore, p is negative and, in fact, p = −ρ.

A major outstanding problem is that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum, up to 120 orders of magnitude too large. This would need to be cancelled almost, but not exactly, by an equally large term of the opposite sign. Some supersymmetric theories require a cosmological constant that is exactly zero, which does not help. This is the cosmological constant problem, the worst problem of fine-tuning in physics: there is no known natural way to derive, even roughly, the infinitesimal cosmological constant observed in cosmology from particle physics. Some physicists, including Steven Weinberg, think the delicate balance of quantum vacuum energy is best explained by the anthropic principle.

In spite of its problems, the cosmological constant is in many respects the most economical solution to the problem of cosmic acceleration. One number successfully explains a multitude of observations. Thus, the current standard model of cosmology, the Lambda-CDM model, includes the cosmological constant as an essential feature.


Alternatively, dark energy might arise from the particle-like excitations in some type of dynamical field, referred to as quintessence. Quintessence differs from the cosmological constant in that it can vary in space and time. In order for it not to clump and form structure like matter, it must be very light so that it has a large Compton wavelength.

No evidence of quintessence is yet available, but it cannot be ruled out either. It generally predicts a slightly slower acceleration of the expansion of the universe than the cosmological constant. Some workers think that the best evidence for quintessence would come from violations of Einstein's equivalence principle and variation of the fundamental constants in space or time. Scalar fields are predicted by the standard model and string theory, but an analogous problem to the cosmological constant problem (or the problem of constructing models of cosmic inflation) occurs: renormalization theory predicts that scalar fields should acquire large masses.

The cosmic coincidence problem asks why the cosmic acceleration begins when it did. If cosmic acceleration began earlier in the universe, structures such as galaxies would never have had time to form and life, at least as we know it, would never have had a chance to exist. Proponents of the anthropic principle view this as support for their arguments. However, many models of quintessence have a so-called tracker behavior, which solves this problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until matter-radiation equality, which triggers quintessence to start behaving as dark energy, eventually dominating the universe. This naturally sets the low energy scale of the dark energy.

Some special cases of quintessence are phantom energy, in which the energy density of quintessence actually increases with time, and k-essence (short for kinetic quintessence) which has a non-standard form of kinetic energy. They can have unusual properties: phantom energy, for example, can cause a Big Rip.

Other ideas

Some theorists think that dark energy and cosmic acceleration are a failure of general relativity on very large scales, larger than superclusters. It is a tremendous extrapolation to think that our theory of gravity, which works so well in the solar system, should work without correction on the scale of the universe. However, most attempts at modifying general relativity have turned out either to be equivalent to theories of quintessence, or are inconsistent with observations.

Other ideas for dark energy have come from string theory, brane cosmology and the holographic principle, but have not yet proved as compelling as quintessence and the cosmological constant.

Implications for the fate of the universe

Cosmologists estimate that the acceleration began roughly 5 billion years ago. Before that, it is thought that the expansion was decelerating, due to the attractive influence of dark matter and baryons. The density of dark matter in an expanding universe disappears more quickly than dark energy, and eventually the dark energy dominates. Specifically, when the volume of the universe doubles, the density of dark matter is halved but the density of dark energy is nearly unchanged (it is exactly constant in the case of a cosmological constant).

If the acceleration continues indefinitely, the ultimate result will be that galaxies outside the local supercluster will move beyond the cosmic horizon: they will no longer be visible, because their relative speed becomes greater than the speed of light. This is not a violation of special relativity, and the effect cannot be used to send a signal between them. (Actually there is no way to even define "relative speed" in a curved spacetime. Relative speed and velocity can only be meaningfully defined in flat spacetime or in sufficiently small (infinitesimal) regions of curved spacetime). Rather, it prevents any communication between them and the objects pass out of contact. The Earth, the Milky Way and the Virgo supercluster, however, would remain virtually undisturbed while the rest of the universe recedes. In this scenario, the local supercluster would ultimately suffer heat death, just as was thought for the flat, matter-dominated universe, before measurements of cosmic acceleration.

There are some very speculative ideas about the future of the universe. One suggests that phantom energy causes divergent expansion, which would imply that the effective force of dark energy continues growing until it dominates all other forces in the universe. Under this scenario, dark energy would ultimately tear apart all gravitationally bound structures, including galaxies and solar systems, and eventually overcome the electrical and nuclear forces to tear apart atoms themselves, ending the universe in a Big Rip. On the other hand, dark energy might dissipate with time, or even become attractive. Such uncertainties leave open the possibility that gravity might yet rule the day and lead to a universe that contracts in on itself in a "Big Crunch". Some scenarios, such as the cyclic model suggest this could be the case. While these ideas are not supported by observations, they are not ruled out. Measurements of acceleration are crucial to determining the ultimate fate of the universe in big bang theory.


The cosmological constant was first proposed by Einstein as a mechanism to obtain a stable solution of the gravitational field equation that would lead to a static universe, effectively using dark energy to balance gravity. Not only was the mechanism an inelegant example of fine-tuning, it was soon realized that Einstein's static universe would actually be unstable because local inhomogeneities would ultimately lead to either the runaway expansion or contraction of the universe. The equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting. These sorts of disturbances are inevitable, due to the uneven distribution of matter throughout the universe. More importantly, observations made by Edwin Hubble showed that the universe appears to be expanding and not static at all. Einstein famously referred to his failure to predict the expanding universe as his greatest blunder. After this realization, the cosmological constant was largely ignored as a historical curiosity.

Alan Guth proposed in the 1970s that a negative pressure field, similar in concept to dark energy, could drive cosmic inflation in the very early universe. Inflation postulates that some repulsive force, qualitatively similar to dark energy, resulted in an enormous and exponential expansion of the universe slightly after the Big Bang. Such expansion is an essential feature of most current models of the Big Bang. However, inflation must have occurred at a much higher energy density than the dark energy we observe today and is believed to have completely ended when the universe was just a fraction of a second old. It is unclear what relation, if any, exists between dark energy and inflation. Even after inflationary models became accepted, the cosmological constant was believed to be irrelevant to the current universe.

By 1998, the missing mass problem of big bang nucleosynthesis and large scale structure was established, and some cosmologists had started to theorize that there was an additional component to our universe, with properties very similar to dark energy. This suspicion was reinforced by supernova observations of accelerated expansion, simultaneously released by the teams of Riess et al and Perlmutter et al. This resulted in the Lambda-CDM model, which as of 2005 has remained consistent with a series of increasingly rigorous cosmological observations.


See also

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