Dark energy

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Eric Linder (2008), Scholarpedia, 3(2):4900. doi:10.4249/scholarpedia.4900 revision #135531 [link to/cite this article]
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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/cm3 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).

Figure 1: Observers' view of the accelerating universe. The apparent brightness of supernovae gives a measure of the distance away and time taken for the light to reach us (horizontal axis), while the redshift of their spectra measures the expansion factor or change in average distance between galaxies or any points in space (vertical axis). Points shown in white are supernovae data that led to the 1998 discovery of the accelerating universe: they clearly lie on a curve in the blue region that requires a recent period of acceleration.

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.

Figure 2: Theorists' view of the accelerating universe. Curves represent the expansion history of different cosmological models (here the cosmological constant \(\Lambda\ ,\) an extra dimension braneworld scenario, and a vacuum metamorphosis or quantum phase transition), and the diagram presents a unified picture of some important properties. The value of a point on a curve measures the conformal horizon, basically the size of the universe, as a function of the cosmic expansion factor. The slope of the curve gives the deceleration parameter \(q\ ;\) if it is positive (up to the right) then the universe is decelerating but if the slope is negative (down to the right) the universe is accelerating. The area under a curve gives the distance measured by observers from the present (\(a=1\) or \(\ln a=0\) to some time in the past when the supernova exploded. The shading around the \(\Lambda\) curve shows how well next generation experiments should probe dark energy.

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.


  • 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

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

External links

See also

Cosmological Constant, Quintessence

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