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In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. Assuming that the lambda-CDM model of cosmology is correct, dark energy is the dominant component of the universe, contributing 68% of the total energy in the present-day observable universe while dark matter and ordinary (baryonic) matter contribute 26% and 5%, respectively, and other components such as neutrinos and photons are nearly negligible. Dark energy's density is very low: 6×10−10 J/m3 (≈7×10−30 g/cm3), much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.
The first observational evidence for dark energy's existence came from measurements of supernovae. Type 1A supernovae have constant luminosity, which means they can be used as accurate distance measures. Comparing this distance to the redshift (which measures the speed at which the supernova is receding) shows that the universe's expansion is accelerating. Prior to this observation, scientists thought that the gravitational attraction of matter and energy in the universe would cause the universe's expansion to slow over time. Since the discovery of accelerating expansion, several independent lines of evidence have been discovered that support the existence of dark energy.
The exact nature of dark energy remains a mystery, and explanations abound. The main candidates are a cosmological constant (representing a constant energy density filling space homogeneously) and scalar fields (dynamic quantities having energy densities that vary in time and space) such as quintessence or moduli. A cosmological constant would remain constant across time and space, while scalar fields can vary. Yet other possibilities are interacting dark energy, an observational effect, and cosmological coupling (see the Theories of Dark Energy section).
History of discovery and previous speculation
Einstein's cosmological constant
The "cosmological constant" is a constant term that can be added to Einstein field equations of general relativity. If considered as a "source term" in the field equation, it can be viewed as equivalent to the mass of empty space (which conceptually could be either positive or negative), or "vacuum energy".
The cosmological constant was first proposed by Einstein as a mechanism to obtain a solution to the gravitational field equation that would lead to a static universe, effectively using dark energy to balance gravity. Einstein gave the cosmological constant the symbol Λ (capital lambda). Einstein stated that the cosmological constant required that 'empty space takes the role of gravitating negative masses which are distributed all over the interstellar space'.
The mechanism was an example of fine-tuning, and it was later realized that Einstein's static universe would not be stable: local inhomogeneities would ultimately lead to either the runaway expansion or contraction of the universe. The equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting. According to Einstein, "empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear, thereby causing accelerated expansion. These sorts of disturbances are inevitable, due to the uneven distribution of matter throughout the universe. Further, observations made by Edwin Hubble in 1929 showed that the universe appears to be expanding and is not static. Einstein reportedly referred to his failure to predict the idea of a dynamic universe, in contrast to a static universe, as his greatest blunder.
Inflationary dark energy
Alan Guth and Alexei Starobinsky proposed in 1980 that a negative pressure field, similar in concept to dark energy, could drive cosmic inflation in the very early universe. Inflation postulates that some repulsive force, qualitatively similar to dark energy, resulted in an enormous and exponential expansion of the universe slightly after the Big Bang. Such expansion is an essential feature of most current models of the Big Bang. However, inflation must have occurred at a much higher (negative) energy density than the dark energy we observe today, and inflation is thought to have completely ended when the universe was just a fraction of a second old. It is unclear what relation, if any, exists between dark energy and inflation. Even after inflationary models became accepted, the cosmological constant was thought to be irrelevant to the current universe.
Nearly all inflation models predict that the total (matter+energy) density of the universe should be very close to the critical density. During the 1980s, most cosmological research focused on models with critical density in matter only, usually 95% cold dark matter (CDM) and 5% ordinary matter (baryons). These models were found to be successful at forming realistic galaxies and clusters, but some problems appeared in the late 1980s: in particular, the model required a value for the Hubble constant lower than preferred by observations, and the model under-predicted observations of large-scale galaxy clustering. These difficulties became stronger after the discovery of anisotropy in the cosmic microwave background by the COBE spacecraft in 1992, and several modified CDM models came under active study through the mid-1990s: these included the Lambda-CDM model and a mixed cold/hot dark matter model. The first direct evidence for dark energy came from supernova observations in 1998 of accelerated expansion in Riess et al. and in Perlmutter et al., and the Lambda-CDM model then became the leading model. Soon after, dark energy was supported by independent observations: in 2000, the BOOMERanG and Maxima cosmic microwave background experiments observed the first acoustic peak in the cosmic microwave background, showing that the total (matter+energy) density is close to 100% of critical density. Then in 2001, the 2dF Galaxy Redshift Survey gave strong evidence that the matter density is around 30% of critical. The large difference between these two supports a smooth component of dark energy making up the difference. Much more precise measurements from WMAP in 2003–2010 have continued to support the standard model and give more accurate measurements of the key parameters.
Change in expansion over time
High-precision measurements of the expansion of the universe are required to understand how the expansion rate changes over time and space. In general relativity, the evolution of the expansion rate is estimated from the curvature of the universe and the cosmological equation of state (the relationship between temperature, pressure, and combined matter, energy, and vacuum energy density for any region of space). Measuring the equation of state for dark energy is one of the biggest efforts in observational cosmology today. Adding the cosmological constant to cosmology's standard FLRW metric leads to the Lambda-CDM model, which has been referred to as the "standard model of cosmology" because of its precise agreement with observations.
As of 2013, the Lambda-CDM model is consistent with a series of increasingly rigorous cosmological observations, including the Planck spacecraft and the Supernova Legacy Survey. First results from the SNLS reveal that the average behavior (i.e., equation of state) of dark energy behaves like Einstein's cosmological constant to a precision of 10%. Recent results from the Hubble Space Telescope Higher-Z Team indicate that dark energy has been present for at least 9 billion years and during the period preceding cosmic acceleration.
The nature of dark energy is more hypothetical than that of dark matter, and many things about it remain in the realm of speculation. Dark energy is thought to be very homogeneous and not dense, and is not known to interact through any of the fundamental forces other than gravity. Since it is rarefied and un-massive—roughly 10−27 kg/m3—it is unlikely to be detectable in laboratory experiments. The reason dark energy can have such a profound effect on the universe, making up 68% of universal density in spite of being so dilute, is that it is believed to uniformly fill otherwise empty space.
The vacuum energy, that is, the particle-antiparticle pairs generated and mutually annihilated within a time frame in accord with Heisenberg's uncertainty principle in the energy-time formulation, has been often invoked as the main contribution to dark energy. The mass–energy equivalence postulated by general relativity implies that the vacuum energy should exert a gravitational force. Hence, the vacuum energy is expected to contribute to the cosmological constant, which in turn impinges on the accelerated expansion of the universe. However, the cosmological constant problem asserts that there is a huge disagreement between the observed values of vacuum energy density and the theoretical large value of zero-point energy obtained by quantum field theory. The cosmological constant problem remains unresolved.
Independently of its actual nature, dark energy would need to have a strong negative pressure to explain the observed acceleration of the expansion of the universe. According to general relativity, the pressure within a substance contributes to its gravitational attraction for other objects just as its mass density does. This happens because the physical quantity that causes matter to generate gravitational effects is the stress–energy tensor, which contains both the energy (or matter) density of a substance and its pressure. In the Friedmann–Lemaître–Robertson–Walker metric, it can be shown that a strong constant negative pressure (i.e., tension) in all the universe causes an acceleration in the expansion if the universe is already expanding, or a deceleration in contraction if the universe is already contracting. This accelerating expansion effect is sometimes labeled "gravitational repulsion".
In standard cosmology, there are three components of the universe: matter, radiation, and dark energy. Matter is anything whose energy density scales with the inverse cube of the scale factor, i.e., ρ ∝ a−3, while radiation is anything which scales to the inverse fourth power of the scale factor (ρ ∝ a−4). This can be understood intuitively: for an ordinary particle in a cube-shaped box, doubling the length of an edge of the box decreases the density (and hence energy density) by a factor of eight (23). For radiation, the decrease in energy density is greater, because an increase in spatial distance also causes a redshift.
The final component is dark energy: it is an intrinsic property of space and has a constant energy density, regardless of the dimensions of the volume under consideration (ρ ∝ a0). Thus, unlike ordinary matter, it is not diluted by the expansion of space.
Evidence of existence
The evidence for dark energy is indirect but comes from three independent sources:
- Distance measurements and their relation to redshift, which suggest the universe has expanded more in the latter half of its life.
- The theoretical need for a type of additional energy that is not matter or dark matter to form the observationally flat universe (absence of any detectable global curvature).
- Measures of large-scale wave patterns of mass density in the universe.
In 1998, the High-Z Supernova Search Team published observations of Type Ia ("one-A") supernovae. In 1999, the Supernova Cosmology Project followed by suggesting that the expansion of the universe is accelerating. The 2011 Nobel Prize in Physics was awarded to Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess for their leadership in the discovery.
Since then, these observations have been corroborated by several independent sources. Measurements of the cosmic microwave background, gravitational lensing, and the large-scale structure of the cosmos, as well as improved measurements of supernovae, have been consistent with the Lambda-CDM model. Some people argue that the only indications for the existence of dark energy are observations of distance measurements and their associated redshifts. Cosmic microwave background anisotropies and baryon acoustic oscillations serve only to demonstrate that distances to a given redshift are larger than would be expected from a "dusty" Friedmann–Lemaître universe and the local measured Hubble constant.
Supernovae are useful for cosmology because they are excellent standard candles across cosmological distances. They allow researchers to measure the expansion history of the universe by looking at the relationship between the distance to an object and its redshift, which gives how fast it is receding from us. The relationship is roughly linear, according to Hubble's law. It is relatively easy to measure redshift, but finding the distance to an object is more difficult. Usually, astronomers use standard candles: objects for which the intrinsic brightness, or absolute magnitude, is known. This allows the object's distance to be measured from its actual observed brightness, or apparent magnitude. Type Ia supernovae are the best-known standard candles across cosmological distances because of their extreme and consistent luminosity.
The theory of large-scale structure, which governs the formation of structures in the universe (stars, quasars, galaxies and galaxy groups and clusters), also suggests that the density of matter in the universe is only 30% of the critical density.
A 2011 survey, the WiggleZ galaxy survey of more than 200,000 galaxies, provided further evidence towards the existence of dark energy, although the exact physics behind it remains unknown. The WiggleZ survey from the Australian Astronomical Observatory scanned the galaxies to determine their redshift. Then, by exploiting the fact that baryon acoustic oscillations have left voids regularly of ≈150 Mpc diameter, surrounded by the galaxies, the voids were used as standard rulers to estimate distances to galaxies as far as 2,000 Mpc (redshift 0.6), allowing for accurate estimate of the speeds of galaxies from their redshift and distance. The data confirmed cosmic acceleration up to half of the age of the universe (7 billion years) and constrain its inhomogeneity to 1 part in 10. This provides a confirmation to cosmic acceleration independent of supernovae.
Cosmic microwave background
The existence of dark energy, in whatever form, is needed to reconcile the measured geometry of space with the total amount of matter in the universe. Measurements of cosmic microwave background anisotropies indicate that the universe is close to flat. For the shape of the universe to be flat, the mass–energy density of the universe must be equal to the critical density. The total amount of matter in the universe (including baryons and dark matter), as measured from the cosmic microwave background spectrum, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the remaining 70%. The Wilkinson Microwave Anisotropy Probe (WMAP) spacecraft seven-year analysis estimated a universe made up of 72.8% dark energy, 22.7% dark matter, and 4.5% ordinary matter. Work done in 2013 based on the Planck spacecraft observations of the cosmic microwave background gave a more accurate estimate of 68.3% dark energy, 26.8% dark matter, and 4.9% ordinary matter.
Late-time integrated Sachs–Wolfe effect
Accelerated cosmic expansion causes gravitational potential wells and hills to flatten as photons pass through them, producing cold spots and hot spots on the cosmic microwave background aligned with vast supervoids and superclusters. This so-called late-time Integrated Sachs–Wolfe effect (ISW) is a direct signal of dark energy in a flat universe. It was reported at high significance in 2008 by Ho et al. and Giannantonio et al.
Observational Hubble constant data
The Hubble constant, H(z), is measured as a function of cosmological redshift. OHD directly tracks the expansion history of the universe by taking passively evolving early-type galaxies as "cosmic chronometers". From this point, this approach provides standard clocks in the universe. The core of this idea is the measurement of the differential age evolution as a function of redshift of these cosmic chronometers. Thus, it provides a direct estimate of the Hubble parameter
The reliance on a differential quantity, Δz/Δt, brings more information and is appealing for computation: It can minimize many common issues and systematic effects. Analyses of supernovae and baryon acoustic oscillations (BAO) are based on integrals of the Hubble parameter, whereas Δz/Δt measures it directly. For these reasons, this method has been widely used to examine the accelerated cosmic expansion and study properties of dark energy.
Theories of dark energy
Dark energy's status as a hypothetical force with unknown properties makes it an active target of research. The problem is attacked from a variety of angles, such as modifying the prevailing theory of gravity (general relativity), attempting to pin down the properties of dark energy, and finding alternative ways to explain the observational data.
The simplest explanation for dark energy is that it is an intrinsic, fundamental energy of space. This is the cosmological constant, usually represented by the Greek letter Λ (Lambda, hence the name Lambda-CDM model). Since energy and mass are related according to the equation E = mc2, Einstein's theory of general relativity predicts that this energy will have a gravitational effect. It is sometimes called a vacuum energy because it is the energy density of empty space – a vacuum.
A major outstanding problem is that the same quantum field theories predict a huge cosmological constant, about 120 orders of magnitude too large. This would need to be almost, but not exactly, cancelled by an equally large term of the opposite sign.
Some supersymmetric theories require a cosmological constant that is exactly zero. Also, it is unknown if there is a metastable vacuum state in string theory with a positive cosmological constant, and it has been conjectured by Ulf Danielsson et al. that no such state exists. This conjecture would not rule out other models of dark energy, such as quintessence, that could be compatible with string theory.
In quintessence models of dark energy, the observed acceleration of the scale factor is caused by the potential energy of a dynamical field, referred to as quintessence field. Quintessence differs from the cosmological constant in that it can vary in space and time. In order for it not to clump and form structure like matter, the field must be very light so that it has a large Compton wavelength. In the simplest scenarios, the quintessence field has a canonical kinetic term, is minimally coupled to gravity, and does not feature higher order operations in its Lagrangian.
No evidence of quintessence is yet available, nor has it been ruled out. It generally predicts a slightly slower acceleration of the expansion of the universe than the cosmological constant. Some scientists think that the best evidence for quintessence would come from violations of Einstein's equivalence principle and variation of the fundamental constants in space or time. Scalar fields are predicted by the Standard Model of particle physics and string theory, but an analogous problem to the cosmological constant problem (or the problem of constructing models of cosmological inflation) occurs: renormalization theory predicts that scalar fields should acquire large masses.
The coincidence problem asks why the acceleration of the Universe began when it did. If acceleration began earlier in the universe, structures such as galaxies would never have had time to form, and life, at least as we know it, would never have had a chance to exist. Proponents of the anthropic principle view this as support for their arguments. However, many models of quintessence have a so-called "tracker" behavior, which solves this problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until matter–radiation equality, which triggers quintessence to start behaving as dark energy, eventually dominating the universe. This naturally sets the low energy scale of the dark energy.
In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that the equation of state had possibly crossed the cosmological constant boundary (w = −1) from above to below. A no-go theorem has been proved that this scenario requires models with at least two types of quintessence. This scenario is the so-called Quintom scenario.
Some special cases of quintessence are phantom energy, in which the energy density of quintessence actually increases with time, and k-essence (short for kinetic quintessence) which has a non-standard form of kinetic energy such as a negative kinetic energy. They can have unusual properties: phantom energy, for example, can cause a Big Rip.
Interacting dark energy
This class of theories attempts to come up with an all-encompassing theory of both dark matter and dark energy as a single phenomenon that modifies the laws of gravity at various scales. This could, for example, treat dark energy and dark matter as different facets of the same unknown substance, or postulate that cold dark matter decays into dark energy. Another class of theories that unifies dark matter and dark energy are suggested to be covariant theories of modified gravities. These theories alter the dynamics of spacetime such that the modified dynamics stems to what have been assigned to the presence of dark energy and dark matter. Dark energy could in principle interact not only with the rest of the dark sector, but also with ordinary matter. However, cosmology alone is not sufficient to effectively constrain the strength of the coupling between dark energy and baryons, so that other indirect techniques or laboratory searches have to be adopted. It was briefly theorized in the early 2020s that excess observed in the XENON1T detector in Italy may have been caused by a chameleon model of dark energy, but further experiments disproved this possibility.
Variable dark energy models
The density of dark energy might have varied in time during the history of the universe. Modern observational data allows us to estimate the present density of dark energy. Using baryon acoustic oscillations, it is possible to investigate the effect of dark energy in the history of the Universe, and constrain parameters of the equation of state of dark energy. To that end, several models have been proposed. One of the most popular models is the Chevallier–Polarski–Linder model (CPL). Some other common models are (Barboza & Alcaniz. 2008), (Jassal et al. 2005), (Wetterich. 2004), and (Oztas et al. 2018).
Some alternatives to dark energy, such as inhomogeneous cosmology, aim to explain the observational data by a more refined use of established theories. In this scenario, dark energy doesn't actually exist, and is merely a measurement artifact. For example, if we are located in an emptier-than-average region of space, the observed cosmic expansion rate could be mistaken for a variation in time, or acceleration. A different approach uses a cosmological extension of the equivalence principle to show how space might appear to be expanding more rapidly in the voids surrounding our local cluster. While weak, such effects considered cumulatively over billions of years could become significant, creating the illusion of cosmic acceleration, and making it appear as if we live in a Hubble bubble. Yet other possibilities are that the accelerated expansion of the universe is an illusion caused by the relative motion of us to the rest of the universe, or that the statistical methods employed were flawed. A laboratory direct detection attempt failed to detect any force associated with dark energy.
Observational skepticism explanations of dark energy have generally not gained much traction among cosmologists. For example, a paper that suggested the anisotropy of the local Universe has been misrepresented as dark energy was quickly countered by another paper claiming errors in the original paper. Another study questioning the essential assumption that the luminosity of Type Ia supernovae does not vary with stellar population age was also swiftly rebutted by other cosmologists.
As a general relativistic effect due to black holes
This theory was formulated by University of Hawaiʻi at Mānoa researchers in February 2023. The idea is that if one requires the Kerr metric (which describes rotating black holes) to asymptote to the Friedmann-Robertson-Walker metric (which describes the isotropic and homogeneous universe that is the basic assumption of modern cosmology), then one finds that black holes gain mass as the universe expands. The rate is measured to be ∝a3, where a is the scale factor. This particular rate means that the energy density of black holes remain constant over time, mimicking dark energy (see Dark_energy#Technical_definition). The theory is called "cosmological coupling" because the black holes couple to a cosmological requirement. Other astrophysicists are skeptical, with a variety of papers claiming that the theory fails to explain other observations.
Other mechanism driving acceleration
The evidence for dark energy is heavily dependent on the theory of general relativity. Therefore, it is conceivable that a modification to general relativity also eliminates the need for dark energy. There are many such theories, and research is ongoing. The measurement of the speed of gravity in the first gravitational wave measured by non-gravitational means (GW170817) ruled out many modified gravity theories as explanations to dark energy.
Astrophysicist Ethan Siegel states that, while such alternatives gain mainstream press coverage, almost all professional astrophysicists are confident that dark energy exists, and that none of the competing theories successfully explain observations to the same level of precision as standard dark energy.
Implications for the fate of the universe
Cosmologists estimate that the acceleration began roughly 5 billion years ago.[a] Before that, it is thought that the expansion was decelerating, due to the attractive influence of matter. The density of dark matter in an expanding universe decreases more quickly than dark energy, and eventually the dark energy dominates. Specifically, when the volume of the universe doubles, the density of dark matter is halved, but the density of dark energy is nearly unchanged (it is exactly constant in the case of a cosmological constant).
Projections into the future can differ radically for different models of dark energy. For a cosmological constant, or any other model that predicts that the acceleration will continue indefinitely, the ultimate result will be that galaxies outside the Local Group will have a line-of-sight velocity that continually increases with time, eventually far exceeding the speed of light. This is not a violation of special relativity because the notion of "velocity" used here is different from that of velocity in a local inertial frame of reference, which is still constrained to be less than the speed of light for any massive object (see Uses of the proper distance for a discussion of the subtleties of defining any notion of relative velocity in cosmology). Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.
However, because of the accelerating expansion, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future because the light never reaches a point where its "peculiar velocity" toward us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in Uses of the proper distance). Assuming the dark energy is constant (a cosmological constant), the current distance to this cosmological event horizon is about 16 billion light years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event were less than 16 billion light years away, but the signal would never reach us if the event were more than 16 billion light years away.
As galaxies approach the point of crossing this cosmological event horizon, the light from them will become more and more redshifted, to the point where the wavelength becomes too large to detect in practice and the galaxies appear to vanish completely (see Future of an expanding universe). Planet Earth, the Milky Way, and the Local Group of galaxies of which the Milky Way is a part, would all remain virtually undisturbed as the rest of the universe recedes and disappears from view. In this scenario, the Local Group would ultimately suffer heat death, just as was hypothesized for the flat, matter-dominated universe before measurements of cosmic acceleration.
There are other, more speculative ideas about the future of the universe. The phantom energy model of dark energy results in divergent expansion, which would imply that the effective force of dark energy continues growing until it dominates all other forces in the universe. Under this scenario, dark energy would ultimately tear apart all gravitationally bound structures, including galaxies and solar systems, and eventually overcome the electrical and nuclear forces to tear apart atoms themselves, ending the universe in a "Big Rip". On the other hand, dark energy might dissipate with time or even become attractive. Such uncertainties leave open the possibility of gravity eventually prevailing and lead to a universe that contracts in on itself in a "Big Crunch", or that there may even be a dark energy cycle, which implies a cyclic model of the universe in which every iteration (Big Bang then eventually a Big Crunch) takes about a trillion (1012) years. While none of these are supported by observations, they are not ruled out.
In philosophy of science
The astrophysicist David Merritt identifies dark energy as an example of an "auxiliary hypothesis", an ad hoc postulate that is added to a theory in response to observations that falsify it. He argues that the dark energy hypothesis is a conventionalist hypothesis, that is, a hypothesis that adds no empirical content and hence is unfalsifiable in the sense defined by Karl Popper. However, his opinion doesn't seem to be consensus[by whom?] and is at odds with the history of cosmology.[why?]
- Taken from Frieman, Turner, & Huterer (2008):: 6, 44
"The Universe has gone through three distinct eras:
- Radiation-dominated, z ≳ 3000 ;
- Matter-dominated, 3000 ≳ z ≳ 0.5 ; and
- Dark-energy-dominated, 0.5 ≳ z .
- : 6
- w ≈ −1 ± 0.1 [stat.] ± 0.1 [sys.] ,
- Idicherian Lonappan, Anto; Kumar, Sumit; R, Ruchika; Ananda Sen, Anjan (21 February 2018). "Bayesian evidences for dark energy models in light of current observational data". Physical Review D. 97 (4): 043524. arXiv:1707.00603. Bibcode:2018PhRvD..97d3524L. doi:10.1103/PhysRevD.97.043524. S2CID 119249858.
- Ade, P. A. R.; Aghanim, N.; Alves, M. I. R.; et al. (Planck Collaboration) (22 March 2013). "Planck 2013 results. I. Overview of products and scientific results – Table 9". Astronomy and Astrophysics. 571: A1. arXiv:1303.5062. Bibcode:2014A&A...571A...1P. doi:10.1051/0004-6361/201321529. S2CID 218716838.
- Ade, P. A. R.; Aghanim, N.; Alves, M. I. R.; et al. (Planck Collaboration) (31 March 2013). "Planck 2013 Results Papers". Astronomy and Astrophysics. 571: A1. arXiv:1303.5062. Bibcode:2014A&A...571A...1P. doi:10.1051/0004-6361/201321529. S2CID 218716838. Archived from the original on 23 March 2013.
- "First Planck results: the Universe is still weird and interesting". 21 March 2013. Archived from the original on 2 May 2019. Retrieved 14 June 2017.
- Sean Carroll, Ph.D., Caltech, 2007, The Teaching Company, Dark Matter, Dark Energy: The Dark Side of the Universe, Guidebook Part 2. p. 46. Retrieved 7 October 2013, "...dark energy: A smooth, persistent component of invisible energy, thought to make up about 70 percent of the current energy density of the universe. Dark energy is known to be smooth because it doesn't accumulate preferentially in galaxies and clusters..."
- Steinhardt, Paul J.; Turok, Neil (2006). "Why the cosmological constant is small and positive". Science. 312 (5777): 1180–1183. arXiv:astro-ph/0605173. Bibcode:2006Sci...312.1180S. doi:10.1126/science.1126231. PMID 16675662. S2CID 14178620.
- "Dark Energy". Hyperphysics. Archived from the original on 27 May 2013. Retrieved 4 January 2014.
- Ferris, Timothy (January 2015). "Dark Matter(Dark Energy)". Archived from the original on 10 June 2015. Retrieved 10 June 2015.
- Overbye, Dennis (20 February 2017). "Cosmos Controversy: The Universe Is Expanding, but How Fast?". The New York Times. Archived from the original on 4 April 2019. Retrieved 21 February 2017.
- Peebles, P. J. E.; Ratra, Bharat (2003). "The cosmological constant and dark energy". Reviews of Modern Physics. 75 (2): 559–606. arXiv:astro-ph/0207347. Bibcode:2003RvMP...75..559P. doi:10.1103/RevModPhys.75.559. S2CID 118961123.
- "Moon findings muddy the water". Archived from the original on 22 November 2016. Retrieved 21 November 2016.
- Carroll, Sean (2001). "The cosmological constant". Living Reviews in Relativity. 4 (1): 1. arXiv:astro-ph/0004075. Bibcode:2001LRR.....4....1C. doi:10.12942/lrr-2001-1. PMC 5256042. PMID 28179856. Archived from the original on 13 October 2006. Retrieved 28 September 2006.
- Harvey, Alex (2012). "How Einstein Discovered Dark Energy". arXiv:1211.6338 [physics.hist-ph].
- "Volume 7: The Berlin Years: Writings, 1918-1921 (English translation supplement) page 31". einsteinpapers.press.princeton.edu. Retrieved 18 September 2023.
- O'Raifeartaigh, C.; O'Keeffe, M.; Nahm, W.; Mitton, S. (2017). 'Einstein's 1917 Static Model of the Universe: A Centennial Review'. Eur. Phys. J. (H) 42: 431–474.
- "Dark Energy, Dark Matter". Science Mission Directorate. 6 March 2012. Archived from the original on 5 November 2020. Retrieved 17 September 2022.
- Gamow, George (1970) My World Line: An Informal Autobiography. p. 44: "Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life." – Here the "cosmological term" refers to the cosmological constant in the equations of general relativity, whose value Einstein initially picked to ensure that his model of the universe would neither expand nor contract; if he hadn't done this he might have theoretically predicted the universal expansion that was first observed by Edwin Hubble.
- Riess, Adam G.; Filippenko; Challis; Clocchiatti; Diercks; Garnavich; Gilliland; Hogan; Jha; Kirshner; Leibundgut; Phillips; Reiss; Schmidt; Schommer; Smith; Spyromilio; Stubbs; Suntzeff; Tonry (1998). "Observational evidence from supernovae for an accelerating universe and a cosmological constant". Astronomical Journal. 116 (3): 1009–1038. arXiv:astro-ph/9805201. Bibcode:1998AJ....116.1009R. doi:10.1086/300499. S2CID 15640044.
- Perlmutter, S.; Aldering; Goldhaber; Knop; Nugent; Castro; Deustua; Fabbro; Goobar; Groom; Hook; Kim; Kim; Lee; Nunes; Pain; Pennypacker; Quimby; Lidman; Ellis; Irwin; McMahon; Ruiz-Lapuente; Walton; Schaefer; Boyle; Filippenko; Matheson; Fruchter; et al. (1999). "Measurements of Omega and Lambda from 42 high redshift supernovae". Astrophysical Journal. 517 (2): 565–586. arXiv:astro-ph/9812133. Bibcode:1999ApJ...517..565P. doi:10.1086/307221. S2CID 118910636.
- The first appearance of the term "dark energy" is in the article with another cosmologist and Turner's student at the time, Dragan Huterer, "Prospects for Probing the Dark Energy via Supernova Distance Measurements", which was posted to the ArXiv.org e-print archive in August 1998 Archived 22 June 2017 at the Wayback Machine and published in Huterer, D.; Turner, M. (1999). "Prospects for probing the dark energy via supernova distance measurements". Physical Review D. 60 (8): 081301. arXiv:astro-ph/9808133. Bibcode:1999PhRvD..60h1301H. doi:10.1103/PhysRevD.60.081301. S2CID 12777640., although the manner in which the term is treated there suggests it was already in general use. Cosmologist Saul Perlmutter has credited Turner with coining the term in an article Archived 11 August 2006 at the Wayback Machine they wrote together with Martin White, where it is introduced in quotation marks as if it were a neologism. Perlmutter, S.; Turner, M.; White, M. (1999). "Constraining Dark Energy with Type Ia Supernovae and Large-Scale Structure". Physical Review Letters. 83 (4): 670–673. arXiv:astro-ph/9901052. Bibcode:1999PhRvL..83..670P. doi:10.1103/PhysRevLett.83.670. S2CID 119427069.
- Astier, Pierre (Supernova Legacy Survey); Guy; Regnault; Pain; Aubourg; Balam; Basa; Carlberg; Fabbro; Fouchez; Hook; Howell; Lafoux; Neill; Palanque-Delabrouille; Perrett; Pritchet; Rich; Sullivan; Taillet; Aldering; Antilogus; Arsenijevic; Balland; Baumont; Bronder; Courtois; Ellis; Filiol; et al. (2006). "The Supernova legacy survey: Measurement of ΩM, ΩΛ and W from the first year data set". Astronomy and Astrophysics. 447 (1): 31–48. arXiv:astro-ph/0510447. Bibcode:2006A&A...447...31A. doi:10.1051/0004-6361:20054185. S2CID 119344498.
- Overbye, Dennis (22 July 2003). "Astronomers Report Evidence of 'Dark Energy' Splitting the Universe". The New York Times. Archived from the original on 26 June 2015. Retrieved 5 August 2015.
- Rugh, S.E.; Zinkernagel, H. (2002). "The quantum vacuum and the cosmological constant problem". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 33 (4): 663–705. arXiv:hep-th/0012253. Bibcode:2002SHPMP..33..663R. doi:10.1016/S1355-2198(02)00033-3. S2CID 9007190. Archived from the original on 30 November 2010. Retrieved 29 October 2022.
- Baumann, Daniel. "Cosmology: Part III Mathematical Tripos, Cambridge University" (PDF). p. 21−22. Archived from the original (PDF) on 2 February 2017. Retrieved 31 January 2017.
- Durrer, R. (2011). "What do we really know about Dark Energy?". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 369 (1957): 5102–5114. arXiv:1103.5331. Bibcode:2011RSPTA.369.5102D. doi:10.1098/rsta.2011.0285. PMID 22084297. S2CID 17562830.
- The first paper, using observed data, which claimed a positive Lambda term was Paál, G.; et al. (1992). "Inflation and compactification from galaxy redshifts?". Astrophysics and Space Science. 191 (1): 107–124. Bibcode:1992Ap&SS.191..107P. doi:10.1007/BF00644200. S2CID 116951785.
- "The Nobel Prize in Physics 2011". Nobel Foundation. Archived from the original on 1 August 2012. Retrieved 4 October 2011.
- The Nobel Prize in Physics 2011 Archived 4 October 2011 at the Wayback Machine. Perlmutter got half the prize, and the other half was shared between Schmidt and Riess.
- Spergel, D. N.; et al. (WMAP collaboration) (June 2007). "Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology" (PDF). The Astrophysical Journal Supplement Series. 170 (2): 377–408. arXiv:astro-ph/0603449. Bibcode:2007ApJS..170..377S. CiteSeerX 10.1.1.472.2550. doi:10.1086/513700. S2CID 1386346. Archived (PDF) from the original on 6 April 2020. Retrieved 26 December 2019.
- Durrer, R. (2011). "What do we really know about dark energy?". Philosophical Transactions of the Royal Society A. 369 (1957): 5102–5114. arXiv:1103.5331. Bibcode:2011RSPTA.369.5102D. doi:10.1098/rsta.2011.0285. PMID 22084297. S2CID 17562830.
- Kowalski, Marek; Rubin, David; Aldering, G.; Agostinho, R. J.; Amadon, A.; Amanullah, R.; Balland, C.; Barbary, K.; Blanc, G.; Challis, P. J.; Conley, A.; Connolly, N. V.; Covarrubias, R.; Dawson, K. S.; Deustua, S. E.; Ellis, R.; Fabbro, S.; Fadeyev, V.; Fan, X.; Farris, B.; Folatelli, G.; Frye, B. L.; Garavini, G.; Gates, E. L.; Germany, L.; Goldhaber, G.; Goldman, B.; Goobar, A.; Groom, D. E.; et al. (27 October 2008). "Improved Cosmological Constraints from New, Old and Combined Supernova Datasets". The Astrophysical Journal. 686 (2): 749–778. arXiv:0804.4142. Bibcode:2008ApJ...686..749K. doi:10.1086/589937. S2CID 119197696.. They find a best-fit value of the dark energy density, ΩΛ of 0.713+0.027–0.029(stat)+0.036–0.039(sys), of the total matter density, ΩM, of 0.274+0.016–0.016(stat)+0.013–0.012(sys) with an equation of state parameter w of −0.969+0.059–0.063(stat)+0.063–0.066(sys).
- "New method 'confirms dark energy'". BBC News. 19 May 2011. Archived from the original on 15 June 2018. Retrieved 21 July 2018.
- Dark energy is real Archived 25 May 2011 at the Wayback Machine, Swinburne University of Technology, 19 May 2011
- "Content of the Universe – Pie Chart". Wilkinson Microwave Anisotropy Probe. National Aeronautics and Space Administration. Archived from the original on 18 August 2018. Retrieved 9 January 2018.
- "Big Bang's afterglow shows universe is 80 million years older than scientists first thought". The Washington Post. Archived from the original on 22 March 2013. Retrieved 22 March 2013.
- Crittenden; Neil Turok (1996). "Looking for $\Lambda$ with the Rees-Sciama Effect". Physical Review Letters. 76 (4): 575–578. arXiv:astro-ph/9510072. Bibcode:1996PhRvL..76..575C. doi:10.1103/PhysRevLett.76.575. PMID 10061494. S2CID 119012700.
- Ho, Shirley; Hirata; Padmanabhan, Nikhil; Seljak, Uros; Bahcall, Neta (2008). "Correlation of cosmic microwave background with large-scale structure: I. ISW Tomography and Cosmological Implications". Physical Review D. 78 (4): 043519. arXiv:0801.0642. Bibcode:2008PhRvD..78d3519H. doi:10.1103/PhysRevD.78.043519. S2CID 38383124.
- Giannantonio, Tommaso; Scranton, Ryan; Crittenden; Nichol; Boughn; Myers; Richards (2008). "Combined analysis of the integrated Sachs–Wolfe effect and cosmological implications". Physical Review D. 77 (12): 123520. arXiv:0801.4380. Bibcode:2008PhRvD..77l3520G. doi:10.1103/PhysRevD.77.123520. S2CID 21763795.
- Yi, Zelong; Zhang, Tongjie (2007). "Constraints on holographic dark energy models using the differential ages of passively evolving galaxies". Modern Physics Letters A. 22 (1): 41–54. arXiv:astro-ph/0605596. Bibcode:2007MPLA...22...41Y. doi:10.1142/S0217732307020889. S2CID 8220261.
- Wan, Haoyi; Yi, Zelong; Zhang, Tongjie; Zhou, Jie (2007). "Constraints on the DGP Universe Using Observational Hubble parameter". Physics Letters B. 651 (5): 1368–1379. arXiv:0706.2723. Bibcode:2007PhLB..651..352W. doi:10.1016/j.physletb.2007.06.053. S2CID 119125999.
- Ma, Cong; Zhang, Tongjie (2011). "Power of observational Hubble parameter data: a figure of merit exploration". Astrophysical Journal. 730 (2): 74. arXiv:1007.3787. Bibcode:2011ApJ...730...74M. doi:10.1088/0004-637X/730/2/74. S2CID 119181595.
- Zhang, Tongjie; Ma, Cong; Lan, Tian (2010). "Constraints on the dark side of the universe and observational Hubble parameter data". Advances in Astronomy. 2010 (1): 1. arXiv:1010.1307. Bibcode:2010AdAst2010E..81Z. doi:10.1155/2010/184284. S2CID 62885316.
- Simon, Joan; Verde, Licia; Jimenez, Raul (2005). "Constraints on the redshift dependence of the dark energy potential". Physical Review D. 71 (12): 123001. arXiv:astro-ph/0412269. Bibcode:2005PhRvD..71l3001S. doi:10.1103/PhysRevD.71.123001. S2CID 13215290.
- by Ehsan Sadri Astrophysics MSc, Azad University, Tehran
- "Planck reveals an almost perfect universe". Planck. ESA. 21 March 2013. Archived from the original on 6 December 2013. Retrieved 21 March 2013.
- Wess, Julius; Bagger, Jonathan (1992). Supersymmetry and Supergravity. Princeton University Press. ISBN 978-0691025308.
- Wolchover, Natalie (9 August 2018). "Dark energy may be incompatible with string theory". Quanta Magazine. Simons Foundation. Archived from the original on 15 November 2020. Retrieved 2 April 2020.
- Danielsson, Ulf; Van Riet, Thomas (April 2018). "What if string theory has no de Sitter vacua?". International Journal of Modern Physics D. 27 (12): 1830007–1830298. arXiv:1804.01120. Bibcode:2018IJMPD..2730007D. doi:10.1142/S0218271818300070. S2CID 119198922.
- Carroll, Sean M. (1998). "Quintessence and the Rest of the World: Suppressing Long-Range Interactions". Physical Review Letters. 81 (15): 3067–3070. arXiv:astro-ph/9806099. Bibcode:1998PhRvL..81.3067C. doi:10.1103/PhysRevLett.81.3067. ISSN 0031-9007. S2CID 14539052.
- Ratra, Bharat; Peebles, P. J. E. (1988). "Cosmological consequences of a rolling homogeneous scalar field". Phys. Rev. D37 (12): 3406–3427. Bibcode:1988PhRvD..37.3406R. doi:10.1103/PhysRevD.37.3406. PMID 9958635.
- Steinhardt, Paul J.; Wang, Li-Min; Zlatev, Ivaylo (1999). "Cosmological tracking solutions". Phys. Rev. D59 (12): 123504. arXiv:astro-ph/9812313. Bibcode:1999PhRvD..59l3504S. doi:10.1103/PhysRevD.59.123504. S2CID 40714104.
- Cai, Yi-Fu; Saridakis, Emmanuel N.; Setare, Mohammed R.; Xia, Jun-Qing (22 April 2010). "Quintom Cosmology – theoretical implications and observations". Physics Reports. 493 (1): 1–60. arXiv:0909.2776. Bibcode:2010PhR...493....1C. doi:10.1016/j.physrep.2010.04.001. S2CID 118866606.
- Caldwell, R. R. (2002). "A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state". Physics Letters B. 545 (1–2): 23–29. arXiv:astro-ph/9908168. Bibcode:2002PhLB..545...23C. doi:10.1016/S0370-2693(02)02589-3. S2CID 9820570.
- Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (16 September 2021). "Does Hubble Tension Signal a Breakdown in FLRW Cosmology?". Classical and Quantum Gravity. 38 (18): 184001. arXiv:2105.09790. Bibcode:2021CQGra..38r4001K. doi:10.1088/1361-6382/ac1a81. ISSN 0264-9381. S2CID 234790314.
- See dark fluid.
- Marcondes, Rafael J. F. (5 October 2016). "Interacting dark energy models in Cosmology and large-scale structure observational tests". arXiv:1610.01272 [astro-ph.CO].
- Exirifard, Q. (2011). "Phenomenological covariant approach to gravity". General Relativity and Gravitation. 43 (1): 93–106. arXiv:0808.1962. Bibcode:2011GReGr..43...93E. doi:10.1007/s10714-010-1073-6. S2CID 119169726.
- Vagnozzi, Sunny; Visinelli, Luca; Mena, Olga; Mota, David F. (2020). "Do we have any hope of detecting scattering between dark energy and baryons through cosmology?". Monthly Notices of the Royal Astronomical Society. 493 (1): 1139–1152. arXiv:1911.12374. Bibcode:2020MNRAS.493.1139V. doi:10.1093/mnras/staa311.
- "A new dark matter experiment quashed earlier hints of new particles". Science News. 22 July 2022. Archived from the original on 26 August 2022. Retrieved 3 August 2022.
- Aprile, E.; Abe, K.; Agostini, F.; Maouloud, S. Ahmed; Althueser, L.; Andrieu, B.; Angelino, E.; Angevaare, J. R.; Antochi, V. C.; Martin, D. Antón; Arneodo, F. (22 July 2022). "Search for New Physics in Electronic Recoil Data from XENONnT". Physical Review Letters. 129 (16): 161805. arXiv:2207.11330. Bibcode:2022PhRvL.129p1805A. doi:10.1103/PhysRevLett.129.161805. PMID 36306777. S2CID 251040527.
- Chevallier, M; Polarski, D (2001). "Accelerating Universes with Scaling Dark Matter". International Journal of Modern Physics D. 10 (2): 213–224. arXiv:gr-qc/0009008. Bibcode:2001IJMPD..10..213C. doi:10.1142/S0218271801000822. S2CID 16489484.
- Linder, Eric V. (3 March 2003). "Exploring the Expansion History of the Universe". Physical Review Letters. 90 (9): 091301. arXiv:astro-ph/0208512. Bibcode:2003PhRvL..90i1301L. doi:10.1103/PhysRevLett.90.091301. PMID 12689209. S2CID 16219710.
- Barboza, E.M.; Alcaniz, J.S. (2008). "A parametric model for dark energy". Physics Letters B. 666 (5): 415–419. arXiv:0805.1713. Bibcode:2008PhLB..666..415B. doi:10.1016/j.physletb.2008.08.012. S2CID 118306372.
- Jassal, H.K; Bagla, J.S (2010). "Understanding the origin of CMB constraints on Dark Energy". Monthly Notices of the Royal Astronomical Society. 405 (4): 2639–2650. arXiv:astro-ph/0601389. Bibcode:2010MNRAS.405.2639J. doi:10.1111/j.1365-2966.2010.16647.x. S2CID 9144993.
- Wetterich, C. (2004). "Phenomenological parameterization of quintessence". Physics Letters B. 594 (1–2): 17–22. arXiv:astro-ph/0403289. Bibcode:2004PhLB..594...17W. doi:10.1016/j.physletb.2004.05.008. S2CID 119354763.
- Oztas, A.; Dil, E.; Smith, M.L. (2018). "The varying cosmological constant: a new approximation to the Friedmann equations and universe model". Mon. Not. R. Astron. Soc. 476 (1): 451–458. Bibcode:2018MNRAS.476..451O. doi:10.1093/mnras/sty221.
- Oztas, A. (2018). "The effects of a varying cosmological constant on the particle horizon". Mon. Not. R. Astron. Soc. 481 (2): 2228–2234. Bibcode:2018MNRAS.481.2228O. doi:10.1093/mnras/sty2375.
- Wiltshire, David L. (2007). "Exact Solution to the Averaging Problem in Cosmology". Physical Review Letters. 99 (25): 251101. arXiv:0709.0732. Bibcode:2007PhRvL..99y1101W. doi:10.1103/PhysRevLett.99.251101. PMID 18233512. S2CID 1152275.
- Ishak, Mustapha; Richardson, James; Garred, David; Whittington, Delilah; Nwankwo, Anthony; Sussman, Roberto (2008). "Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?". Physical Review D. 78 (12): 123531. arXiv:0708.2943. Bibcode:2008PhRvD..78l3531I. doi:10.1103/PhysRevD.78.123531. S2CID 118801032.
- Mattsson, Teppo (2010). "Dark energy as a mirage". Gen. Rel. Grav. 42 (3): 567–599. arXiv:0711.4264. Bibcode:2010GReGr..42..567M. doi:10.1007/s10714-009-0873-z. S2CID 14226736.
- Clifton, Timothy; Ferreira, Pedro (April 2009). "Does Dark Energy Really Exist?". Scientific American. 300 (4): 48–55. Bibcode:2009SciAm.300d..48C. doi:10.1038/scientificamerican0409-48. PMID 19363920.
- Wiltshire, D. (2008). "Cosmological equivalence principle and the weak-field limit". Physical Review D. 78 (8): 084032. arXiv:0809.1183. Bibcode:2008PhRvD..78h4032W. doi:10.1103/PhysRevD.78.084032. S2CID 53709630.
- Gray, Stuart (8 December 2009). "Dark questions remain over dark energy". ABC Science Australia. Archived from the original on 15 January 2013. Retrieved 27 January 2013.
- Merali, Zeeya (March 2012). "Is Einstein's Greatest Work All Wrong – Because He Didn't Go Far Enough?". Discover magazine. Archived from the original on 28 January 2013. Retrieved 27 January 2013.
- Wolchover, Natalie (27 September 2011) 'Accelerating universe' could be just an illusion Archived 24 September 2020 at the Wayback Machine, NBC News
- Tsagas, Christos G. (2011). "Peculiar motions, accelerated expansion, and the cosmological axis". Physical Review D. 84 (6): 063503. arXiv:1107.4045. Bibcode:2011PhRvD..84f3503T. doi:10.1103/PhysRevD.84.063503. S2CID 119179171.
- Nielsen, J. T.; Guffanti, A.; Sarkar, S. (21 October 2016). "Marginal evidence for cosmic acceleration from Type Ia supernovae". Scientific Reports. 6: 35596. arXiv:1506.01354. Bibcode:2016NatSR...635596N. doi:10.1038/srep35596. PMC 5073293. PMID 27767125.
- Gillespie, Stuart (21 October 2016). "The universe is expanding at an accelerating rate – or is it?". University of Oxford – News & Events – Science Blog (WP:NEWSBLOG). Archived from the original on 26 July 2017. Retrieved 10 August 2017.
- Sabulsky, D. O.; Dutta, I.; Hinds, E. A.; Elder, B.; Burrage, C.; Copeland, E. J. (2019). "Experiment to Detect Dark Energy Forces Using Atom Interferometry". Physical Review Letters. 123 (6): 061102. arXiv:1812.08244. Bibcode:2019PhRvL.123f1102S. doi:10.1103/PhysRevLett.123.061102. PMID 31491160. S2CID 118935116.
- Colin, Jacques; Mohayaee, Roya; Rameez, Mohamed; Sakar, Subir (22 July 2019). "Evidence for anisotropy of cosmic acceleration". Astronomy & Astrophysics. 631: L13. arXiv:1808.04597. Bibcode:2019A&A...631L..13C. doi:10.1051/0004-6361/201936373. S2CID 208175643.
- Rubin, D.; Heitlauf, J. (6 May 2020). "Is the Expansion of the Universe Accelerating? All Signs Still Point to Yes: A Local Dipole Anisotropy Cannot Explain Dark Energy". The Astrophysical Journal. 894 (1): 68. arXiv:1912.02191. Bibcode:2020ApJ...894...68R. doi:10.3847/1538-4357/ab7a16. ISSN 1538-4357. S2CID 208637339.
- Yonsei University (6 January 2020). "New evidence shows that the key assumption made in the discovery of dark energy is in error". Phys.org. Archived from the original on 13 January 2020. Retrieved 6 January 2020.
- Kang, Yijung; et al. (2020). "Early-type Host Galaxies of Type Ia Supernovae. II. Evidence for Luminosity Evolution in Supernova Cosmology". The Astrophysical Journal. 889 (1): 8. arXiv:1912.04903. Bibcode:2020ApJ...889....8K. doi:10.3847/1538-4357/ab5afc. S2CID 209202868.
- Gohd, Chelsea (9 January 2020). "Has Dark Energy Been Debunked? Probably Not". Space.com. Archived from the original on 2 March 2020. Retrieved 14 February 2020.
- "Wait... Did We Finally Find the Source of Dark Energy?!". MSN. Retrieved 4 April 2023.
- Siegel, Ethan (17 February 2023). "Ask Ethan: Can black holes really cause dark energy?". Starts with a Bang.
- Rodriguez, Carl L. "No, black holes are not the source of dark energy". Retrieved 11 September 2023.
- Ghodla, Sohan; Easther, Richard; Briel, M. M.; Eldridge, J. J. (20 July 2023). "Observational implications of cosmologically coupled black holes". The Open Journal of Astrophysics. 6: 25. arXiv:2306.08199. Bibcode:2023OJAp....6E..25G. doi:10.21105/astro.2306.08199. S2CID 259165172.
- See Sami, M.; Myrzakulov, R. (2015). "Late time cosmic acceleration: ABCD of dark energy and modified theories of gravity". International Journal of Modern Physics D. 25 (12): 1630031. arXiv:1309.4188. Bibcode:2016IJMPD..2530031S. doi:10.1142/S0218271816300317. S2CID 119256879. for a recent review
- Joyce, Austin; Lombriser, Lucas; Schmidt, Fabian (2016). "Dark Energy vs. Modified Gravity". Annual Review of Nuclear and Particle Science. 66 (1): 95. arXiv:1601.06133. Bibcode:2016ARNPS..66...95J. doi:10.1146/annurev-nucl-102115-044553. S2CID 118468001.
- Lombriser, Lucas; Lima, Nelson (2017). "Challenges to Self-Acceleration in Modified Gravity from Gravitational Waves and Large-Scale Structure". Physics Letters B. 765: 382–385. arXiv:1602.07670. Bibcode:2017PhLB..765..382L. doi:10.1016/j.physletb.2016.12.048. S2CID 118486016.
- "Quest to settle riddle over Einstein's theory may soon be over". phys.org. 10 February 2017. Archived from the original on 28 October 2017. Retrieved 29 October 2017.
- "Theoretical battle: Dark energy vs. modified gravity". Ars Technica. 25 February 2017. Archived from the original on 28 October 2017. Retrieved 27 October 2017.
- Siegel, Ethan (2018). "What Astronomers Wish Everyone Knew About Dark Matter And Dark Energy". Forbes (Starts With A Bang blog). Archived from the original on 11 April 2018. Retrieved 11 April 2018.
- Frieman, Joshua A.; Turner, Michael S.; Huterer, Dragan (1 January 2008). "Dark Energy and the Accelerating Universe". Annual Review of Astronomy and Astrophysics. 46 (1): 385–432. arXiv:0803.0982. Bibcode:2008ARA&A..46..385F. doi:10.1146/annurev.astro.46.060407.145243. S2CID 15117520.
- Krauss, Lawrence M.; Scherrer, Robert J. (March 2008). "The End of Cosmology?". Scientific American. 82. Archived from the original on 19 March 2011. Retrieved 6 January 2011.
- Is the universe expanding faster than the speed of light? Archived 23 November 2003 at the Wayback Machine (see the last two paragraphs)
- Lineweaver, Charles; Davis, Tamara M. (2005). "Misconceptions about the Big Bang" (PDF). Scientific American. Archived from the original (PDF) on 19 July 2011. Retrieved 6 November 2008.
- Loeb, Abraham (2002). "The Long-Term Future of Extragalactic Astronomy". Physical Review D. 65 (4): 047301. arXiv:astro-ph/0107568. Bibcode:2002PhRvD..65d7301L. doi:10.1103/PhysRevD.65.047301. S2CID 1791226.
- Krauss, Lawrence M.; Scherrer, Robert J. (2007). "The Return of a Static Universe and the End of Cosmology". General Relativity and Gravitation. 39 (10): 1545–1550. arXiv:0704.0221. Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9. S2CID 123442313.
- Using Tiny Particles To Answer Giant Questions Archived 6 May 2018 at the Wayback Machine. Science Friday, 3 April 2009. According to the transcript Archived 6 May 2018 at the Wayback Machine, Brian Greene makes the comment "And actually, in the far future, everything we now see, except for our local galaxy and a region of galaxies will have disappeared. The entire universe will disappear before our very eyes, and it's one of my arguments for actually funding cosmology. We've got to do it while we have a chance."
- How the Universe Works 3. Vol. End of the Universe. Discovery Channel. 2014.
- "'Cyclic universe' can explain cosmological constant". New Scientist. Retrieved 18 September 2023.
- Steinhardt, P. J.; Turok, N. (25 April 2002). "A Cyclic Model of the Universe". Science. 296 (5572): 1436–1439. arXiv:hep-th/0111030. Bibcode:2002Sci...296.1436S. doi:10.1126/science.1070462. PMID 11976408. S2CID 1346107.
- Merritt, David (2017). "Cosmology and convention". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 57: 41–52. arXiv:1703.02389. Bibcode:2017SHPMP..57...41M. doi:10.1016/j.shpsb.2016.12.002. S2CID 119401938.
- Helbig, Phillip (2020). "Sonne und Mond, or, the good, the bad, and the ugly: comments on the debate between MOND and LambdaCDM". The Observatory. 140: 225–247. Bibcode:2020Obs...140..225H.