Dark energy

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.

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. As such, the fraction of dark energy to 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. He called it the cosmological constant Λ.It featured in his field equations of general relativity to represent an energy uniform in space and constant in time, necessary for his static universeassumption at the time.

In 1927, Georges Lemaître provided an expanding-universe solution to Edwin Hubble's 1929 distance–velocity relation,, proving beyond doubt that the universe is constantly expanding, not static. Therefore, the cosmological constant was no longer necessary in the field equations of general relativity, but it remained available as an ingredient of cosmological models.

type Ia supernovae and measurement of the cosmological constant

In the simplest Big Bang models, the expansion of a matter-filled universe should decelerate: gravity pulls every galaxy towards every other, slowing the expansion set going by the Big Bang.

Validating this theory via practical measurement was difficult. Accurate measurements of the rate of expansion of the universe require objects whose intrinsic brightness is known well enough that their apparent brightness reveals their distance, nicknamed standard candles by cosmologists.

During the 1990s, two teams, the High-Z Supernova Search Team and the Supernova Cosmology Project, used type Ia supernovae as standard candles to trace the expansion history of the universe over the last several billion years.

In 1998, the High-Z team, led by Adam Riess and Brian Schmidt, 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.

One year later, the Supernova Cosmology Project, led by Saul Perlmutter, published its 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.

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. The remaining roughly 68% must be a smooth component that does not cluster like matter, in agreement with the supernova result: dark energy.

Large-scale structure and baryon acoustic oscillations

Another independent class of evidence comes from the growth of large-scale structure. In the early universe, pressure waves travelled through the hot plasma until recombination, leaving a characteristic scale, the baryon acoustic oscillation (BAO) scale, imprinted in the clustering of galaxies. Measuring the BAO scale at different cosmic epochs, together with the growth of structure itself, traces the expansion history 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.

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}

Since its pressure is

p = −ρc² 

We have

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.

Multiple hypothesis on the nature of the 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. Because of this problem, many cosmologists suspect that dark energy is more subtle than something that can be described by a bare constant.

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

Au lieu of introducing a slowly-evolving scalar field, other scientists argue that the accelerating cosmic expansion signals rather 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.

Further reading

• The Universe, NASA Science
• Planck, European Space Agency
• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, Riess et al. (1998)
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae, Perlmutter et al. (1999)