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]
Assuming the existence of dark energy is the most popular way to explain recent observations that the universe appears to be
expanding at an accelerating
rate. In the standard model of cosmology, dark energy currently accounts for
almost three-quarters of the total mass-energy of the universe.
Two proposed forms for dark energy are the cosmological constant, a constant
energy density filling space homogeneously,[2] and scalar fields such as quintessence or moduli, dynamic fields whose energy density can
vary in time and space. In fact contributions from scalar fields which are constant
in space are usually also included in the cosmological constant. The
cosmological constant is thought to arise from the vacuum energy. Scalar fields which do change in space are hard to distinguish from a cosmological
constant, because the change may be extremely slow.
High-precision measurements of the expansion of the universe are required
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 the cosmological constant to cosmology's standard FLRW
metric leads to the Lambda-CDM model, which has been referred to as the
"standard model" of cosmology because of its precise agreement with observations.
Dark energy has been used as a crucial ingredient in a recent attempt [3] to formulate a cyclic model for the universe.
Negative pressure
Strangely, dark energy causes expansion because it has strong negative
pressure.
A substance has positive pressure when it pushes outward on its surroundings. This is the usual situation for fluids. Negative
pressure, or tension, exists when the substance instead pulls on its surroundings. A common example of negative pressure occurs
when a solid is stretched to support a hanging weight.
According to the Friedmann-Lemaître-Robertson-Walker
metric, which is an application of General Relativity to cosmology, the
pressure within a substance contributes to its gravitational attraction for other things just as its mass density does. Negative
pressure causes a gravitational repulsion.
The gravitational repulsive effect of dark energy's negative pressure is greater than the gravitational attraction caused by
the energy itself. At the cosmological scale, it also overwhelms all other forms of gravitational attraction, resulting in the
accelerating expansion of the universe.
One might wonder, how can pushing cause attraction? How can pulling cause repulsion? This sounds like a contradiction. The
solution is:
- The pushing of positive pressure (and the pulling of negative pressure) are non-gravitational forces which just move
substances around within space without changing space itself.
- But the gravitational attraction (or repulsion) they cause operates on space itself, decreasing (or increasing) the
amount of space between things. It is this which determines the size of the universe.
- There is no necessity that these two effects should act in the same direction. In fact, they act in opposite directions.
Evidence for dark energy
In 1998, observations of type Ia supernovae ("one-A") by the Supernova Cosmology Project at the Lawrence Berkeley National Laboratory and the High-z Supernova Search Team suggested that the expansion of the universe is accelerating.[4][5] Since then, these observations have been corroborated by several independent sources.
Measurements of the cosmic microwave background, gravitational lensing, and the large scale
structure of the cosmos as well as improved measurements of supernovae have been consistent with the Lambda-CDM model.[6]
The type Ia supernovae provide the most direct evidence for dark energy. Measuring the scale factor at the time that light was
emitted from an object 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 actual brightness, what astronomers call the absolute magnitude, is known, so that it is possible to relate the observed brightness, or
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 thus visible across billions of light years.
The consistency in absolute magnitude for type Ia supernovae is explained by the favored model of an old white dwarf star which gains mass from a companion star and grows until it reaches the precisely defined
Chandrasekhar limit. At this mass, the white
dwarf is unstable to thermonuclear runaway and explodes as a type Ia supernova with a characteristic brightness. The
observed brightness of the supernovae are plotted against their redshifts, and this is used to measure the expansion history of
the universe. These observations indicate that the expansion of 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, is needed to reconcile the measured geometry of space with the total amount of
matter in the universe. Measurements of the cosmic microwave
background (CMB), most recently by the WMAP satellite,
indicate that the universe is very close to flat. For the shape of the universe to
be flat, the mass/energy density of the Universe must be equal to a certain
critical density. The total amount of matter in the Universe (including
baryons and dark matter), as measured by the CMB, accounts
for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the
remaining 70%.[6]
The theory of large scale structure, which governs the formation
of structure in the universe (stars, quasars, galaxies and galaxy clusters), also suggests that the density
of matter in the universe is only 30% of the critical density.
The most recent WMAP observations are consistent with a Universe made up of 74% dark energy, 22% dark matter, and 4% ordinary
matter.
Nature of dark energy
As this NASA chart indicates, roughly 70 percent or more of the universe consists of dark energy, about which we know next to
nothing.
The exact nature of this dark energy is a matter of speculation. It is known to be very homogeneous, not very dense and is not known to interact 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. 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, a volume of space has some
intrinsic, fundamental energy. This is the cosmological constant, sometimes called Lambda (hence Lambda-CDM model) after the Greek letter Λ, the symbol used to mathematically represent this quantity.
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; Energy must be lost from inside a container to do work on the container. A change in volume dV requires
work done equal to a change of energy −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 (rho) 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. The present scientific consensus amounts to extrapolating the empirical evidence where it is relevant to predictions, and fine-tuning
theories until a more elegant solution is found. Philosophically, our most elegant solution may be to say that if things were
different, we would not be here to observe anything - the anthropic
principle.[7] Technically, this amounts to checking
theories against macroscopic observations. Unfortunately, as the known error margin in the constant predicts the fate of the universe more than its present state, many such "deeper" questions remain
unknown.
Another problem arises with inclusion of the cosmic constant in the standard model which is appearance of solutions with
regions of discontinuities (see classification of
discontinuities for three examples) at low matter density.[8] The discontinuity also affects the past sign of the vacuum energy, changing from the current
negative pressure to attractive, as one looks back towards the early Universe. This finding should be considered a shortcoming of
the standard model, but only when a term for vacuum energy is included.
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.
Quintessence
Dark energy may become dark matter when buffeted by baryonic particles, thus leading to
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 has not been ruled out either. It generally predicts a slightly slower
acceleration of the expansion of the universe than the cosmological constant. Some scientists 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 began 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.
See main article on quintessence
Alternative 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 law of gravity, which works so well in
the solar system, should work without correction on the scale of the universe. Most
attempts at modifying general relativity, however, have turned out to be either equivalent to theories of quintessence, or inconsistent with observations.
Alternative 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.
Yet another, "radically conservative" class of proposals aims to explain the observational data by a more refined use of
established theories rather than through the introduction of dark energy, focusing, for example, on the gravitational effects of
density inhomogeneities (assumed negligible in the standard Friedmann-Robertson-Walker approximation and confirmed negligible by studies
of the anisotropies of the cosmic microwave background and
statistics of large-scale structure) or on consequences of
electroweak symmetry breaking in the early universe[9].
More insight as to dark energy might be deduced from LIGO I (with it's 10-21 sensitivity), Virgo etc. non-detection
of gravity waves; which might be interpreted as indicating that CR pseudo-Riemannian spacetime continuum (manifold's)
stiffness is not insignificant, rather than the assumption that g.w.s propagate long distance. Statistically LIGO I seems to have
a large enough volume and sample size for inclusion of compact objects in NS and BH binary systems in tight orbits at least, even
if not catching any coalescing events. However even for binary coalescence of BHs, generated {g.w.} might decay very rapidly. So
resistance to deformation (normal stress: extension and compression, and even any shear stress) might not be insignificant. Such
stiffness (resistance to deformation/distortion) may be considered as like inertia of CR manifold. That is, {g.w.}
have non-localized energy, but such energy is associated with deformation of manifold. Hence such {g.w.} energy might be
considered as trying to overcome resistance to deformation (i.e. stiffness) of CR manifold. Hence such inertia of
manifold (resistance to deformation) would seem to represent a contribution to stress energy momentum tensor and it’s matrix
representation; thus contributing not insignificantly to overall curvature. So if long range g.w.s are not detected, then LIGO I
might actually be exploring a qualitative assessment (not limits) as to stiffness of CR manifold. Thus CR
manifold may be quite robust to perturbation. Any such robustness would seem consistent with such manifold not breaking up (i.e.
so no "foam"?) for near to, and at Cp Planck scale; hence also consistent with no quantization of manifold
CR. Also then less likely to have leakage of g.w.s propagating out of CR manifold into another dimension
i.e. brane. Also any such significant stiffness of CR manifold would be less consistent with deformations associated
with superstrings. And if the concept of inertia of manifold is descriptive, then any entertained recent new acceleration (i.e.
resulting then in a strain or elasticity of manifold) of such CR manifold would seem less likely. Also energy
associated with resistance to deformation of manifold may represent a significant portion of energy required to approach
flatness. That is, rather than a quest for so-called dark energy, perhaps an additional significant contribution is in the form
of energy of CR manifold; such stiffness of CR manifold contributing to stress energy momentum tensor, and
hence to curvature. So perhaps LIGO I already has made a great discovery - that is, the inertia of CR manifold. So
CR manifold seems to have significant stiffness, and hence contributes a significant amount of energy to Tuv, and thus
contributes significantly to curvature.[10][11]
Implications for the fate of the universe
Cosmologists estimate that the acceleration began roughly 9 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 line-of-sight velocity 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.
History
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 idea of a dynamic universe, in contrast to a static universe, as
his greatest blunder. Following 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 thought 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 thought to be irrelevant to the current universe.
The term "dark energy" was coined by Michael Turner in 1998.[12] By that time, 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. The first direct evidence for dark energy came from supernova observations of accelerated expansion, in Riess et al[5] and later confirmed in Perlmutter et al.[4]. This resulted in the Lambda-CDM model, which as
of 2006 is consistent with a series of increasingly rigorous cosmological observations, the latest being the 2005 Supernova
Legacy Survey. First results from the SNLS reveal that the average behavior (i.e., equation of state) of dark energy behaves like
Einstein's cosmological constant to a precision of 10 per cent.[13] Recent results from the Hubble Space Telescope Higher-Z Team indicate that dark energy has been
present for at least 9 billion years and during the period preceding cosmic acceleration.
References
- ^ P. J. E. Peebles and Bharat
Ratra (2003). "The cosmological constant
and dark energy". Reviews of Modern Physics 75: 559–606.
- ^ Sean Carroll (2001). "The cosmological constant". Living Reviews in Relativity 4. Retrieved on
2006-09-28.
- ^ L.Baum and P.H. Frampton
(2007). "Turnaround in Cyclic
Cosmology". Physical Review Letters 98: 071301.
- ^ a b S.
Perlmutter et al. (The Supernova Cosmology Project) (1999).
"Measurements of Omega and Lambda from
42 high redshift supernovae". Astrophysical J. 517: 565–86.
- ^ a b Adam G.
Riess et al. (Supernova Search Team) (1998). "Observational evidence from supernovae for an
accelerating universe and a cosmological constant". Astronomical J. 116: 1009–38.
- ^ a b D. N. Spergel et al. (WMAP collaboration)
(March 2006). "Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology".
- ^ S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev.
Lett. 59, 2607 (1987).
- ^ A.M. Öztas and M.L. Smith (2006).
"Elliptical Solutions to the Standard Cosmology Model with Realistic Values of Matter Density". International Journal of
Theoretical Physics 45: 925-936.
- ^ Primordial inflation explains why the universe is accelerating today by Kolb, Matarrese, Notari and Riotto,
which is disputed by [1],
[2] and [3]
- ^ http://www.tmmalm.info
- ^ See Phenomenology - Alternative Models and Theory - Alternative Models at INFN/Torino for an actively maintained list of recent work in this rapidly
evolving field.
- ^ The first mention of the term "dark energy" is in the article with another
cosmologist and Turner's student at the time, Dragan Huterer, "Prospects for Probing the Dark Energy via Supernova Distance
Measurements", which was posted to the ArXiv.org e-print archive in August 1998 and published in
Physical Review D in 1999 (Huterer and Turner, Phys. Rev. D 60, 081301 (1999)).
- ^ Pierre Astier et al.
(Supernova Legacy Survey) (2006). "The Supernova legacy survey: Measurement of
omega(m), omega(lambda) and W from the first year data set". Astronomy and Astrophysics 447:
31–48.
Bibliography
- HubbleSite press release: New Clues About the Nature of Dark Energy: Einstein May Have Been Right After All.
- 1998 paper announcing the dark energy discovery: Riess et al
- 1999 paper confirming dark energy discovery Perlmutter et al.
- The group that first detected cosmic acceleration: High-Z supernova search
team and the group that confirmed it Supernova
Cosmology Project.
- Sean Carroll's technical reviews: Why is the universe accelerating?, The Cosmological Constant, and Dark Energy and the Preposterous Universe.
- Jim Peebles, Testing General
Relativity on the Scales of Cosmology.
- "The World's Most Successful Nearby Supernova Search Engine", The Katzman Automatic Imaging Telescope.
- Supernova Acceleration Probe (SNAP), a proposed
satellite experiment.
- A reanalysis ([4],
[5]) of
an experiment [R.H. Koch, D. van Harlingen, J. Clarke, Phys. Rev. B 26 (1982) 74] to find the broad-band spectrum of
Josephson-junction noise current claims to connect it to the spectral frequency upper limit predicted by matching estimates of
the dark energy density to the measured vacuum energy density. This claim is not yet accepted. For disputes, see [6], [7], [8].
- Christopher J. Coneslice, "The Universe's Invisible Hand," Scientific American. February, 2007.
See also
Further reading and external links
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