Dark energy: Difference between revisions

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Dark energy is a theorised form of energy that explains the accelerating expansion of the Universe. According to the standard model of cosmology, it is the largest single ingredient of the universe, making up about 68% of the total mass–energy content of the universe.^[1]

Dark energy, unlike ordinary matter and energy, is not gathered into galaxies and clusters by gravity but spread almost uniformly throughout space. Furthermore, while ordinary matter and energy are diluted by the expansion of the universe, the density of dark energy in space changes very slowly as the universe expands.^[2] As such, the fraction of dark energy in the content of the universe has grown over time, causing it to increasingly dominate the dynamics of the cosmos.

History

The cosmological constant and the expanding universe

The first theoretical ancestor of dark energy was introduced by Albert Einstein in 1917, who called it the cosmological constant, usually written Λ. It featured in his field equations of general relativity as an energy uniform in space and constant in time, necessary for the static universe assumed at the time.

10 years later, the discovery that the universe is expanding rendered the constant unnecessary. Following the mathematical work of Alexander Friedmann, Georges Lemaître derived in 1927 an expanding-universe solution of general relativity and connected the expansion to the redshift of distant galaxies, obtaining a linear distance–radial-velocity relation. This relation was further established observationally two years later by Edwin Hubble.^[3]^[4] With the universe shown to be expanding rather than static, Einstein's original justification for introducing the constant disappeared: He is said to have later called it his "biggest blunder", and it was dropped from the standard Big Bang models that followed.

Type Ia supernovae and the return of the cosmological constant

With the cosmological constant set to zero, the standard Big Bang models predict that the expansion of the universe must decelerate: gravity pulls every galaxy towards every other, slowing down the expansion initiated by the Big Bang. How strongly the expansion decelerates depends on how much matter the universe contains, so by the 1990s cosmologists were attempting to measure the deceleration, expecting to find that the expansion was slowing down.

Measuring the expansion history requires objects whose intrinsic brightness is known well enough that their apparent brightness reveals their distance, nicknamed standard candles by cosmologists. During the 1990s, type Ia supernovae became the standard candles of choice: they are the explosions of white dwarfs that have accreted matter beyond a critical mass, which makes their peak brightness remarkably uniform. The small remaining differences are corrected by the width–luminosity relation, which links how fast the supernova fades to how bright it is at its peak, turning type Ia supernovae into "standardisable" candles usable out to redshifts of order one.

Two rival teams set out to apply them: the Supernova Cosmology Project, led by Saul Perlmutter, and the High-Z Supernova Search Team, led by Adam Riess and Brian Schmidt. Both expected to observe the deceleration caused by gravity. Instead, both found the opposite.

In 1998, the High-Z team reported the analysis of 16 high-redshift type Ia supernovae together with 34 nearby ones. The high-redshift supernovae were on average 10–15% farther away than expected in a low-density universe without a cosmological constant, and the data unanimously favoured eternally expanding models with a positive cosmological constant, ΩΛ > 0, and a currently accelerating expansion.^[5] One year later, the Supernova Cosmology Project published the analysis of 42 type Ia supernovae at redshifts between 0.18 and 0.83. The data indicated that the cosmological constant is non-zero and positive, with 99% confidence.^[6]

Both teams had therefore measured not a deceleration but an acceleration of the cosmic expansion. Within general relativity, such an acceleration requires a dominant component with negative pressure, precisely what a cosmological constant, or something like it, would provide. The constant had returned, this time under the name of dark energy.

Saul Perlmutter, Brian Schmidt and Adam Riess shared the 2011 Nobel Prize in Physics for the discovery of the accelerating expansion of the universe through observations of distant supernovae.

The history of the universe, from the Big Bang to the present day. The expansion first slowed under the pull of matter and radiation, then accelerated as dark energy came to dominate. Credit: NASA/WMAP Science Team (public domain).

The term dark energy was coined in analogy with dark matter: like that component it is invisible, and the name is intended to leave open what the new ingredient actually is.

Additional observational evidence

The cosmic microwave background

The cosmic microwave background (CMB) offers an independent measurement of the geometry and content of the universe. The final full-mission Planck measurements, published in 2020, are consistent with a spatially flat universe whose total density is close to the critical density, but in which ordinary and dark matter together contribute only about 31% of that density.^[1] The remaining roughly 68% must be a smooth component that does not cluster like matter, in agreement with the supernova result: dark energy.^[1]

Large-scale structure and baryon acoustic oscillations

Another independent class of evidence comes from the way galaxies are distributed in space. In the hot early universe, matter and light were tightly coupled, and pressure waves, in effect sound waves, rippled outward from every overdense region. When the universe cooled enough for atoms to form, matter and light decoupled, and those ripples froze into the distribution of matter. The consequence is visible today in galaxy surveys: two galaxies are slightly more likely to be separated by one particular distance, about 150 megaparsecs (roughly 500 million light-years), than by any other. Cosmologists call this preferred spacing the baryon acoustic oscillation (BAO) scale. Because its true length is known from the CMB, it acts as a cosmic standard ruler: measuring how this ruler appears in surveys at different distances, and therefore at different times in cosmic history, traces the expansion history of the universe and the competition between the pull of matter and the push of dark energy. Combined with the CMB, these measurements confirm the energy budget inferred from supernovae and pin down the equation of state of dark energy.^[1]

The physics of dark energy

Under the assumptions of homogeneity and isotropy on large scales, the expansion of the universe is described by the Friedmann equations, which follow from general relativity:

H^2 = \frac{8\pi G}{3}\rho - \frac{k c^2}{a^2} + \frac{\Lambda c^2}{3}

\frac{\ddot a}{a} = -\frac{4\pi G}{3}\left(\rho + \frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3}

Here a is the scale factor (the Hubble parameter is H = ȧ/a), k the spatial curvature, ρ the total mass density, p the pressure, G the gravitational constant, c the speed of light, and Λ the cosmological constant.

The second equation demonstrates that any fluid with a non-negative pressure, such as ordinary matter (p = 0) or radiation (p = ρc²/3), results in a more negative right-hand side, decelerating the expansion of the universe. The observed acceleration in the rate of expansion of the universe can only be explained by a dominant component with negative pressure satisfying ρ + 3p/c² < 0.

Cosmologists characterise each component by its dimensionless equation-of-state parameter

w = \frac{p}{\rho c^2}

with w = 0 for non-relativistic matter, w = 1/3 for radiation, and w = −1 for a cosmological constant.

Mathematically, any component with w < −1/3 contributes to the acceleration of the rate of expansion of the universe. For this component to dominate the energy budget, it must also dilute more slowly than matter.

The simplest component satisfying w < −1/3 is the cosmological constant itself, which behaves exactly as a fluid of constant energy density

\rho_{\Lambda} = \frac{\Lambda c^2}{8\pi G}

with a constant negative pressure

p = -\rho_\Lambda c^2

so that its equation-of-state parameter is exactly

w = -1

As the universe expands and matter is diluted, such a constant-density component becomes steadily more dominant, explaining why the acceleration of the cosmic expansion began only when the universe was already several billion years old, as dark energy had overtaken matter.^[2]

Multiple hypotheses on the nature of dark energy

The cosmological constant and the vacuum

If dark energy is the cosmological constant, it can be interpreted as the energy of the vacuum: quantum field theory predicts that empty space should carry a vacuum energy that behaves exactly like a cosmological constant. The trouble is its magnitude: naive estimates of the vacuum energy exceed the observed value of Λ by some 120 orders of magnitude, one of the largest discrepancies between theory and observation in physics. This difficulty is known as the cosmological constant problem.^[2] Because of this problem, many cosmologists suspect that dark energy is more subtle than a bare cosmological constant.^[2]

Quintessence

Alternatives propose a dynamical dark energy, in which the acceleration is driven by a slowly-evolving scalar field, called quintessence, whose density declines with time, so that its equation-of-state parameter can differ from −1 and vary over cosmic history.

Modified gravity

Instead of introducing a new energy component, other physicists argue that the accelerating cosmic expansion signals a breakdown of general relativity on cosmological scales, which would require a modified theory of gravity.

Current and future probes

As of September 2026, the nature of dark energy remains a core objective of observational cosmology. The Dark Energy Spectroscopic Instrument (DESI) and the European Space Agency's Euclid space telescope are measuring the expansion history of the universe and the growth of cosmic structure over most of cosmic history, and the Nancy Grace Roman Space Telescope, launched in August 2026, is extending the supernova and weak-lensing measurements to much larger samples. The key observable is the equation-of-state parameter w and its possible variation with time: any deviation from −1 would rule out a pure cosmological constant and point to one of the dynamical alternatives.

References

↑ ↑ ↑ ↑ Planck Collaboration. (2020). Planck 2018 results (Scholarly article). In Astronomy and Astrophysics (Vols. 641, p. A6). https://doi.org/10.1051/0004-6361/201833910
↑ ↑ ↑ ↑ Carroll, S. (2001). The Cosmological Constant (Scholarly article). In Living Reviews in Relativity (Vols. 4, p. 1). https://doi.org/10.12942/lrr-2001-1
↑ Lemaître, G. (1927). Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques (Scholarly article). In Annales de la Société scientifique de Bruxelles (Vols. 47, pp. 49–59).
↑ Hubble, E. (1929). A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae (Scholarly article). In Proceedings of the National Academy of Sciences of the United States of America (Vols. 15, Issues 3, pp. 168–173). https://doi.org/10.1073/pnas.15.3.168
↑ Riess, A. (1998). Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant (Scholarly article). In The Astronomical Journal (Vols. 116, Issues 3, pp. 1009–1038). https://doi.org/10.1086/300499
↑ Perlmutter, S. (1999). Measurements of Omega and Lambda from 42 High-Redshift Supernovae (Scholarly article). In The Astrophysical Journal (Vols. 517, Issues 2, pp. 565–586). https://doi.org/10.1086/307221

@@ Line 11: / Line 11: @@
 The first theoretical ancestor of dark energy was introduced by Albert Einstein in 1917, who called it the '''cosmological constant''', usually written Λ. It featured in his field equations of general relativity as an energy uniform in space and constant in time, necessary for the static universe assumed at the time.
-The discovery that the universe is expanding would soon make the constant unnecessary. Following the mathematical work of Alexander Friedmann, Georges Lemaître derived in 1927 an expanding-universe solution of general relativity and connected the expansion to the redshift of distant galaxies, obtaining the linear distance–radial-velocity relation established observationally two years later by Edwin Hubble.<ref>{{#cite:Q1526}}</ref><ref>{{#cite:Q1527}}</ref> With the universe shown to be expanding rather than static, Einstein's original reason for introducing the constant disappeared; Einstein is said to have later called it his "biggest blunder", and it was dropped from the standard Big Bang models that followed. Its story, however, was not over: the term remained available in the equations, and observations at the end of the 20th century would bring it back.
+years later, the discovery that the universe is expanding rendered the constant unnecessary. Following the mathematical work of Alexander Friedmann, Georges Lemaître derived in 1927 an expanding-universe solution of general relativity and connected the expansion to the redshift of distant galaxies, obtaining a linear distance–radial-velocity relation. This relation was further established observationally two years later by Edwin Hubble.<ref>{{#cite:Q1526}}</ref><ref>{{#cite:Q1527}}</ref> With the universe shown to be expanding rather than static, Einstein's original justification for introducing the constant disappeared: He is said to have later called it his "biggest blunder", and it was dropped from the standard Big Bang models that followed.
 === Type Ia supernovae and the return of the cosmological constant ===