# Dark energy

**Dark energy** is the name given to the unknown physics causing the
current acceleration of the cosmic expansion. Whether dark energy
is truly a new component of energy density or an extension of
gravitational physics beyond general relativity is not yet known.

## Dark universe

The consequences of dark energy for fundamental physics will not be clear until its origin is discovered, but the effects on the universe are dramatic. Dark energy effectively contributes 70-75% of the current energy density of the universe, governing the expansion of space, causing it to accelerate over the last ~5 billion years, and will determine the fate of the universe. Such a phenomenon is not predicted within the standard model of particle physics nor within experimental experience of gravity as an attractive force.

Gravitation as an attractive force acts to slow down the cosmic
expansion, so dark energy acts in this sense as antigravity or
cosmic repulsion. This can however occur within general
relativity for substances with strongly negative pressure
(tension); the **equation of state**, or pressure to energy density,
ratio \(w\) measures this and when \(w<-1/3\)
then the substance acts in a gravitationally repulsive manner.

## Physical origin

### High energy physics origin

The cosmological constant \(\Lambda\) is one such (theorized)
gravitationally repulsive substance, with pressure \(p\) equal
and opposite to its constant energy density \(\rho\ ,\) and so
\(w\equiv p/\rho=-1\ .\) This may be connected to the ground
state energy,
or **vacuum energy** of a quantum field pervading space. Another
possibility is an evolving scalar field arising from high energy
physics - for standard fields this is called quintessence. More
baroque fields with nonstandard dynamics (e.g. k-essence) or with
nongravitational interactions with some forms of matter (e.g. with
dark matter or neutrinos), called coupled dark energy, or with
nonminimal coupling to gravity, e.g. scalar-tensor gravity, have
been postulated as well.

### Gravitational origin

Extending the gravitational physics itself, by changing the Einstein-Hilbert action of general relativity (\(\Lambda\) can enter here as well), is another avenue of exploration. This has two main branches: higher derivative and higher dimension theories. In higher derivative theories, terms with more derivatives of the metric tensor than the two allowed by general relativity are included. These are related to scalar-tensor theories since the extension generically generates additional degrees of freedom including scalar fields.

Higher dimension theories change the nature of spacetime, adding to the three spatial dimensions either large (also called universal) or compact, topologically rolled-up extra dimensions. Examples of universal extra dimension theories include braneworld scenarios where all standard physics except for gravity is restricted to the usual space. Compact extra dimensions arise in Kaluza-Klein theories and give modification of gravity on small length scales, less than a millimeter.

### Outside the standard model

According to Einstein's theory of general relativity, all forms of energy contribute to gravitation. One can think of this as \(E=mc^2\ ,\) that energy sources gravity just as mass does. The particular combination of energies entering into this passive gravitational mass is \(\rho+3p\ ,\) or \(\rho(1+3w)\ ,\) so if the pressure is sufficiently negative (hence \(w<-1/3\)) then the effective mass becomes negative. This breaks the strong energy condition of classical cosmology.

From a particle physics perspective, the dark energy
density measured today of \(7\times 10^{-30}\) g/cm^{3}
corresponds to \((2\times 10^{-3}{\rm eV})^4\ .\) This is not
only some \(10^{-120}\) times smaller than the *natural* scale for
a quantum vacuum energy, the Planck scale of
\((1.2\times 10^{28}{\rm eV})^4\ ,\) but corresponds to no standard
particle physics energy scale. Within a quantum scalar field model for
dark energy, the effective mass of the field must be less than the
Hubble scale, corresponding to \(m\lesssim 10^{-33}\) eV, for
acceleration to have begun recently. Again, such a scale is well outside
standard particle physics. Such a light field would have a Compton
wavelength larger than the Hubble scale and so the dark energy would be
smoothly distributed throughout the universe.

## Detecting dark energy

Dark energy is not detected tangibly because it smoothly permeates
the entire universe. Indeed, in the case of a gravitational
origin there may be no "thing" to detect; dark energy is manifest
only as a change in physical laws, e.g. the inverse square law of
gravitational attraction on certain length scales. Instead astronomers
observe its direct
effects accelerating the cosmic expansion and its indirect effects
through the consequences of the acceleration on the contents of
the universe. Measuring distances as a function of expansion
scale factor \(a\) maps out the cosmic expansion history
\(a(t)\) and quantifies
the deceleration and acceleration. The use of Type Ia supernovae
as standardized light sources - **calibrated candles** - led to the
observational discovery of dark energy by two groups in 1998
(Riess et al. 1998, Perlmutter et al. 1999).

Measurement of the characteristic angle corresponding to the peak of the cosmic microwave background temperature fluctuation power, the acoustic peak scale, served as a calibrated ruler when combined with the overall scale of the universe given by the Hubble constant \(H_0\ ,\) and by 2003 strongly supported the picture of an accelerating universe (Spergel et al. 2003). Use of the acoustic peak scale as imprinted in the pattern of galaxies, called baryon acoustic oscillations, began to give results in 2005, in further corroboration (Eisenstein et al. 2005).

Accelerated expansion can be indirectly measured through its
effect on the growth of large scale structures of matter, the
formation and evolution of galaxies and clusters of galaxies.
Comparing the observed statistical pattern to that from computer
simulations shows that models with dark energy provide much
better matches than those without. The recent accelerated
expansion of space suppresses the growth due to gravitational
attraction, forcing structure to have formed earlier to match
the current pattern. This early growth and later slowdown should
be measurable through the abundance of clusters of various masses at
different epochs, the cluster mass function, although the
processes of galaxy formation and astrophysical effects are not
yet well enough understood to use this robustly. Such a slowdown
in growth is seen in the decay of cluster gravitational potentials
as measured by the integrated Sachs-Wolfe effect; observations give
modest evidence for a breakdown in matter domination, if not
pointing in detail toward acceleration. The evolution
of growth can be measured through the influence of the evolving
gravitational potentials of massive structures on light passing
by - this slight deflection and distortion of shapes of distant
sources is called **weak gravitational lensing**.
The statistical effects of weak lensing were measured in 2000 and
are consistent with, but do not yet independently constrain,
accelerating expansion.

## Probing dark energy

Measurements as of 2008, with the greatest weight coming from the
combination of supernovae with either cosmic microwave background
or baryon acoustic oscillation data, show that dark energy makes
up \(72\pm3\%\) of the total energy density of the universe,
and its equation of state averaged over the last 7 billion years
is \(w=-1.00\pm0.1\) (Kowalski et al. 2008).
This is consistent with the simplest picture, the
cosmological constant, but also with a great many scenarios of
time varying dark energy or extended gravity theories. For the
future, various ground based projects are in the works and being planned
and a space telescope dedicated to exploring dark energy is being
developed, called the **Joint Dark Energy Mission**.

Combining multiple, complementary techniques is regarded as essential for checking for systematic errors in the data and its analysis, for breaking degeneracies between cosmological parameters such as the dark energy density and its equation of state, and for testing the physical origin of the acceleration. Geometric measurements such as distances that probe purely the expansion history can be compared to large scale structure measurements such as gravitational lensing that probe the mass growth history. Distinguishing between a physical dark energy and an extension of the laws of gravitation requires data from both these different classes of measurements.

Probing dark energy is regarded with such import because dark energy in turn probes the foundations of physics - either the nature of the quantum vacuum, the nature of gravity and spacetime, or their unification. By dominating the cosmic energy density dark energy determines the fate of the universe; continued acceleration would lead to an ever less dense and colder universe, with the horizon of the visible universe closing in around each observer, leaving observers in a truly dark universe.

## References

- Eisenstein D.J. et al. (2005) Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies. Astrophys. J. 633:560-574

- Kowalski M. et al. (2008) Improved Cosmological Constraints from New, Old, and Combined Supernova Datasets. Astrophys. J.686, 749

- Perlmutter S. et al. (1999) Measurements of Omega and Lambda from 42 High-Redshift Supernovae. Astrophys. J. 517:565-586

- Riess A.G. et al. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. Astron. J. 116:1009-1038

- Spergel D.N. et al. (2003) First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. Astrophys. J. Suppl. 148:175-194

## Recommended reading

- Linder E.V. (2008) Resource Letter on Dark Energy and the Accelerating Universe. Am. J. Phys. 76, 197-204, arXiv:0705.4102

- Perlmutter S. and Schmidt B.P. (2003) Measuring Cosmology with Supernovae, Lect. Notes Phys. 598:195-217 arXiv.org

- Riess A.G. and Turner M.S. (2004) From Slowdown to Speedup. Sci. Am. 290:62-67