Accelerating expansion of the universe

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The expansion of the universe has been accelerating since the universe entered its dark-energy-dominated era, at redshift z ≈ 0.4 (roughly 5 billion years ago).[3][notes 1] Within the framework of general relativity, an accelerating expansion can be accounted for by a positive value of the cosmological constant Λ, equivalent to the presence of a positive vacuum energy, dubbed "dark energy". While there are alternative possible explanations, the description assuming dark energy (positive Λ) is used in the current standard model of cosmology, known as ΛCDM (lambda cold dark matter).

The accelerated expansion was discovered in 1998, when two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team simultaneously obtained results suggesting an acceleration in the expansion of the universe by using distant type Ia supernovae as standard candles.[4][5][6] The discovery was unexpected, cosmologists at the time expecting a deceleration in the expansion of the universe, and amounts to the realization that the universe is currently in a "dark-energy-dominated era". Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery.[7] Confirmatory evidence has been found in baryon acoustic oscillations and other new results about the clustering of galaxies.



In the decades since the detection of cosmic microwave background (CMB) in 1965,[9] the Big Bang model has become the most accepted model explaining the evolution of our universe. The Friedmann equation defines how the energy in the universe drives its expansion.

where Κ represents the curvature of the universe, a(t) is the scale factor, ρ is the total energy density of the universe, and H is the Hubble parameter.[10]

We define a critical density

and the density parameter

We can then rewrite the Hubble parameter as

where the four currently hypothesized contributors to the energy density of the universe are curvature, matter, radiation and dark energy.[11] Each of the components decreases with the expansion of the universe (increasing scale factor), except perhaps the dark energy term. It is the values of these cosmological parameters which physicists use to determine the acceleration of the universe.

The acceleration equation describes the evolution of the scale factor with time


Physicists at one time were so assured of the deceleration of the universe's expansion that they introduced a so-called deceleration parameter q0.[12][page needed] Current observations point towards this deceleration parameter being negative.

Evidence for acceleration[edit]


Supernova observation[edit]


The first evidence for acceleration came from the observation of Type Ia supernovae, which are exploding white dwarfs that have exceeded their stability limit. Because they all have similar masses, their intrinsic luminosity is standardizable. Repeated imaging of selected areas of sky is used to discover the supernovae, then follow-up observations give their peak brightness, which is converted into a quantity known as luminosity distance (see distance measures in cosmology for details).[13] Spectral lines of their light can be used to determine their redshift.


So a supernova with a measured redshift z = 0.5 implies the universe was 1/1 + 0.5 = 2/3 of its present size when the supernova exploded. In an accelerating universe, the universe was expanding more slowly in the past than it is today, which means it took a longer time to expand from two thirds its present size to its present size compared to a non-accelerating universe. This results in a larger light-travel time, larger distance and fainter supernovae, which corresponds to the actual observations. Riess found that "the distances of the high-redshift SNe Ia were, on average, 10% to 15% farther than expected in a low mass density ΩM = 0.2 universe without a cosmological constant".[14] This means that the measured high-redshift distances were too large, compared to nearby ones, for a decelerating universe.[15]

Baryon acoustic oscillations[edit]


Peaks have been found in the correlation function (the probability that two galaxies will be a certain distance apart) at 100 h−1 Mpc,[11] indicating that this is the size of the sound horizon today, and by comparing this to the sound horizon at the time of decoupling (using the CMB), we can confirm that the expansion of the universe is accelerating.[17]

Clusters of galaxies[edit]

Measuring the mass functions of galaxy clusters, which describe the number density of the clusters above a threshold mass, also provides evidence for dark energy.[18] By comparing these mass functions at high and low redshifts to those predicted by different cosmological models, values for w and Ωm are obtained which confirm a low matter density and a non zero amount of dark energy.[15]

Age of the universe[edit]



Explanatory models[edit]


Dark energy[edit]

Main article: Dark energy


where c is the speed of light and ρ is the energy density. Different theories of dark energy suggest different values of w, with w < −1/3 for cosmic acceleration (this leads to a positive value of ä in the acceleration equation above).

The simplest explanation for dark energy is that it is a cosmological constant or vacuum energy; in this case w = −1. This leads to the Lambda-CDM model, which has generally been known as the Standard Model of Cosmology from 2003 through the present, since it is the simplest model in good agreement with a variety of recent observations. Riess found that their results from supernovae observations favoured expanding models with positive cosmological constant (Ωλ > 0) and a current acceleration of the expansion (q0 < 0).[14]

Phantom energy[edit]

Main article: Phantom energy

Current observations allow the possibility of a cosmological model containing a dark energy component with equation of state w < −1. This phantom energy density would become infinite in finite time, causing such a huge gravitational repulsion that the universe would lose all structure and end in a Big Rip.[19] For example, for w = −3/2 and H0 = 70 km·s−1·Mpc−1, the time remaining before the universe ends in this "Big Rip" is 22 billion years.[20]

Alternative theories[edit]

Other explanations for the accelerating universe include quintessence, a proposed form of dark energy with a non-constant state equation, whose density decreases with time. Dark fluid is an alternative explanation for accelerating expansion which attempts to unite dark matter and dark energy into a single framework.[21] Alternatively, some authors have argued that the universe expansion acceleration could be due to a repulsive gravitational interaction of antimatter.[22][23][24]

Another type of model, the backreaction conjecture,[25][26] was proposed by cosmologist Syksy Räsänen:[27] the rate of expansion is not homogenous, but we are in a region where expansion is faster than the background. Inhomogeneities in the early universe cause the formation of walls and bubbles, where the inside of a bubble has less matter than on average. According to general relativity, space is less curved than on the walls, and thus appears to have more volume and a higher expansion rate. In the denser regions, the expansion is retarded by a higher gravitational attraction. Therefore, the inward collapse of the denser regions looks the same as an accelerating expansion of the bubbles, leading us to conclude that the universe is expanding at an accelerating rate.[28] The benefit is that it does not require any new physics such as dark energy. Räsänen does not consider the model likely, but without any falsification, it must remain a possibility. It would require rather large density fluctuations (20%) to work.[27]

Theories for the consequences to the universe[edit]



A constantly expanding universe with non-zero cosmological constant has mass density decreasing over time, to an undetermined point when zero matter density is reached. All matter (electrons, protons and neutrons) would ionize and disintegrate, with objects dissipating away.[30]

Alternatives for the ultimate fate of the universe include the Big Rip mentioned above, a Big Bounce, Big Freeze, Big Crunch or possible proton decay.

See also[edit]




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  4. ^ "Nobel physics prize honours accelerating universe find". BBC News. 2011-10-04. 
  6. ^ Peebles, P. J. E.; Ratra, Bharat (2003). "The cosmological constant and dark energy". Reviews of Modern Physics. 75 (2): 559–606. arXiv:astro-ph/0207347free to read. Bibcode:2003RvMP...75..559P. doi:10.1103/RevModPhys.75.559. 
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  13. ^ Albrecht, Andreas; Bernstein, Gary; Cahn, Robert; Freedman, Wendy L.; Hewitt, Jacqueline; Hu, Wayne; Huth, John; Kamionkowski, Marc; Kolb, Edward W.; Knox, Lloyd; Mather, John C.; Staggs, Suzanne; Suntzeff, Nicholas B. (2006-09-20). "Report of the Dark Energy Task Force". arXiv:astro-ph/0609591free to read. 
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