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Accelerating expansion of the universe
Accelerating expansion of the universe
Accelerating expansion of the universe
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Lambda-CDM, accelerated expansion of the universe. The timeline in this schematic diagram extends from the Big Bang/inflation era 13.8 billion years ago to the present cosmological time.

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time.[1][2][3] The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration.[4][5][6] The idea was that as type Ia supernovae have almost the same intrinsic brightness (a standard candle), and since objects that are further away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the further away an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. 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 in analyses of the clustering of galaxies.

The accelerated expansion of the universe is thought to have begun since the universe entered its dark-energy-dominated era roughly 5 billion years ago.[8][notes 1] Within the framework of general relativity, an accelerated 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 standard model of cosmology, which also includes cold dark matter (CDM) and is known as the Lambda-CDM model.

Background

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Further information: Cosmological constant, Lambda-CDM model, Hubble's law, Friedmann–Lemaître–Robertson–Walker metric, and Friedmann equations

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]

The critical density is defined as and the density parameter

The Hubble parameter can then be rewritten 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 where the pressure P is defined by the cosmological model chosen (see also: Explanatory models).

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] Recent observations indicate this deceleration parameter is negative.

Relation to inflation

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According to the theory of cosmic inflation, the very early universe underwent a period of very rapid, quasi-exponential expansion. While the time-scale for this period of expansion was far shorter than that of the existing expansion, this was a period of accelerated expansion with some similarities to the current epoch.

Technical definition

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The definition of "accelerating expansion" is that the second time derivative of the cosmic scale factor, , is positive, which is equivalent to the deceleration parameter, , being negative. However, note this does not imply that the Hubble parameter is increasing with time. Since the Hubble parameter is defined as , it follows from the definitions that the derivative of the Hubble parameter is given by so the Hubble parameter is decreasing with time unless . Observations prefer , which implies that is positive but is negative. Essentially, this implies that the cosmic recession velocity of any one particular galaxy is increasing with time, but its velocity/distance ratio is still decreasing; thus different galaxies expanding across a sphere of fixed radius cross the sphere more slowly at later times.

It is seen from above that the case of "zero acceleration/deceleration" corresponds to is a linear function of , , , and .

Evidence for acceleration

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The rate of expansion of the universe can be analyzed using the magnitude-redshift relationship of astronomical objects using standard candles, or their distance-redshift relationship using standard rulers. Also a factor is the growth of large-scale structure, finding that the observed values of the cosmological parameters are best described by models which include an accelerating expansion.

Supernova observation

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Artist's impression of a Type Ia supernova, as revealed by spectro-polarimetry observations

In 1998, the first evidence for acceleration came from the observation of Type Ia supernovae, which are exploding white dwarf stars that have exceeded their stability limit. Because they all have similar masses, their intrinsic luminosity can be standardized. Repeated imaging of selected areas of the 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.

For supernovae at redshift less than around 0.1, or light travel time less than 10 percent of the age of the universe, this gives a nearly linear distance–redshift relation due to Hubble's law. At larger distances, since the expansion rate of the universe has changed over time, the distance-redshift relation deviates from linearity, and this deviation depends on how the expansion rate has changed over time. The full calculation requires computer integration of the Friedmann equation, but a simple derivation can be given as follows: the redshift z directly gives the cosmic scale factor at the time the supernova exploded.

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 the case of accelerated expansion, is positive; therefore, was smaller in the past than today. Thus, an accelerating universe took a longer time to expand from 2/3 to 1 times its present size, compared to a non-accelerating universe with constant and the same present-day value of the Hubble constant. This results in a larger light-travel time, larger distance and fainter supernovae, which corresponds to the actual observations. Adam Riess et al. found that "the distances of the high-redshift SNe Ia were, on average, 10% to 15% further 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]

Several researchers have questioned the majority opinion on the acceleration or the assumption of the "cosmological principle" (that the universe is homogeneous and isotropic).[16] For example, a 2019 paper analyzed the Joint Light-curve Analysis catalog of Type Ia supernovas, containing ten times as many supernova as were used in the 1998 analyses, and concluded that there was little evidence for a "monopole", that is, for an isotropic acceleration in all directions[17][18] (see also: § Alternative theories, below).

Baryon acoustic oscillations

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Main article: Baryon acoustic oscillations

In the early universe before recombination and decoupling took place, photons and matter existed in a primordial plasma. Points of higher density in the photon-baryon plasma would contract, being compressed by gravity until the pressure became too large and they expanded again.[12] This contraction and expansion created vibrations in the plasma analogous to sound waves. Since dark matter only interacts gravitationally, it stayed at the centre of the sound wave, the origin of the original overdensity. When decoupling occurred, approximately 380,000 years after the Big Bang,[19] photons separated from matter and were able to stream freely through the universe, creating the cosmic microwave background as we know it. This left shells of baryonic matter at a fixed radius from the overdensities of dark matter, a distance known as the sound horizon. As time passed and the universe expanded, it was at these inhomogeneities of matter density where galaxies started to form. So by looking at the distances at which galaxies at different redshifts tend to cluster, it is possible to determine a standard angular diameter distance and use that to compare to the distances predicted by different cosmological models.

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] (where h is the dimensionless Hubble constant) 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 the accelerated expansion of the universe.[20]

Clusters of galaxies

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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 [further explanation needed].[21] 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

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See also: Age of the universe

Given a cosmological model with certain values of the cosmological density parameters, it is possible to integrate the Friedmann equations and derive the age of the universe.

By comparing this to actual measured values of the cosmological parameters, we can confirm the validity of a model which is accelerating now, and had a slower expansion in the past.[15]

Gravitational waves as standard sirens

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Recent discoveries of gravitational waves through LIGO and VIRGO[22][23][24] not only confirmed Einstein's predictions but also opened a new window into the universe. These gravitational waves can work as sort of standard sirens to measure the expansion rate of the universe. Abbot et al. 2017 measured the Hubble constant value to be approximately 70 kilometres per second per megaparsec.[22] The amplitudes of the strain 'h' is dependent on the masses of the objects causing waves, distances from observation point and gravitational waves detection frequencies. The associated distance measures are dependent on the cosmological parameters like the Hubble Constant for nearby objects[22] and will be dependent on other cosmological parameters like the dark energy density, matter density, etc. for distant sources.[25][24]

Explanatory models

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The expansion of the Universe accelerating. Time flows from bottom to top

Dark energy

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Main article: Dark energy

The most important property of dark energy is that it has negative pressure (repulsive action) which is distributed relatively homogeneously in space.

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 et al. found that their results from supernova observations favoured expanding models with positive cosmological constant (Ωλ > 0) and an accelerated expansion (q0 < 0).[14]

Phantom energy

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Main article: Phantom energy

These 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.[26] 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.[27]

Alternative theories

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See also: Dark energy § Theories of dark energy, and Dark energy § Alternatives to dark energy

There are many alternative explanations for the accelerating universe. Some examples are quintessence, a proposed form of dark energy with a non-constant state equation, whose density decreases with time. A negative mass cosmology does not assume that the mass density of the universe is positive (as is done in supernova observations), and instead finds a negative cosmological constant. Occam's razor also suggests that this is the 'more parsimonious hypothesis'.[28][29] Dark fluid is an alternative explanation for accelerating expansion which attempts to unite dark matter and dark energy into a single framework.[30] Alternatively, some authors have argued that the accelerated expansion of the universe could be due to a repulsive gravitational interaction of antimatter[31][32][33] or a deviation of the gravitational laws from general relativity, such as massive gravity, meaning that gravitons themselves have mass.[34] The measurement of the speed of gravity with the gravitational wave event GW170817 ruled out many modified gravity theories as alternative explanations to dark energy.[35][36][37] Another type of model, the backreaction conjecture,[38][39] was proposed by cosmologist Syksy Räsänen:[40] the rate of expansion is not homogenous, but Earth is 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 slowed 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 undergoing an accelerated expansion.[41] 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.[40]

Shockwave cosmology, proposed by Joel Smoller and Blake Temple in 2003, has the "big bang" as an explosion inside a black hole, producing the expanding volume of space and matter that includes the observable universe.[42] A related theory by Smoller, Temple, and Vogler proposes that this shockwave may have resulted in our part of the universe having a lower density than that surrounding it, causing the accelerated expansion normally attributed to dark energy.[43][44] They also propose that this related theory could be tested: a universe with dark energy should give a figure for the cubic correction to redshift versus luminosity C = −0.180 at a = a whereas for Smoller, Temple, and Vogler's alternative C should be positive rather than negative. They give a more precise calculation for their shockwave model alternative as: the cubic correction to redshift versus luminosity at a = a is C = 0.359.[44]

Although shockwave cosmology produces a universe that "looks essentially identical to the aftermath of the big bang",[45] cosmologists consider that it needs further development before it could be considered as a more advantageous model than the big bang theory (or standard model) in explaining the universe. In particular, and especially for the proposed alternative to dark energy, it would need to explain big bang nucleosynthesis, the quantitative details of the microwave background anisotropies, the Lyman-alpha forest, and galaxy surveys.[43]

A final possibility is that dark energy is an illusion caused by some bias in measurements. 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.[46][47][48][49] 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.[50][51][52] 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,[53][54] or that the supernova sample size used wasn't large enough.[55][56]

Consequences for the universe

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See also: Future of an expanding universe

As the universe expands, the density of radiation and ordinary dark matter declines more quickly than the density of dark energy (see equation of state) and, eventually, dark energy dominates. Specifically, when the scale of the universe doubles, the density of matter is reduced by a factor of 8, but the density of dark energy is nearly unchanged (it is exactly constant if the dark energy is the cosmological constant).[12]

In models where dark energy is the cosmological constant, the universe will expand exponentially with time in the far future, coming closer and closer to a de Sitter universe. This will eventually lead to all evidence for the Big Bang disappearing, as the cosmic microwave background is redshifted to lower intensities and longer wavelengths. Eventually, its frequency will be low enough that it will be absorbed by the interstellar medium, and so be screened from any observer within the galaxy. This will occur when the universe is less than 50 times its existing age, leading to the end of any life as the distant universe turns dark.[57]

A constantly expanding universe with a non-zero cosmological constant has mass density decreasing over time. Under such a scenario, it is understood that all matter will ionize and disintegrate into isolated stable particles such as electrons and neutrinos, with all complex structures dissipating.[58] This is called "heat death of the universe" (or the Big Freeze).

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

See also

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Notes

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Accelerating expansion of the universe

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The accelerating expansion of the universe is the observed phenomenon in which the rate of expansion of the increased over time starting approximately 5–6 billion years ago, a discovery that revolutionized cosmology by implying the dominance of a repulsive force counteracting gravitational attraction. This acceleration, which followed an initial decelerating phase after the , is primarily attributed to , a mysterious component that permeates space and is thought to have driven the universe's growth at a quickening pace. The evidence for this acceleration first emerged in 1998 from independent observations of distant Type Ia supernovae by the High-Z Supernova Search Team and the Supernova Cosmology Project, which served as "standard candles" to measure cosmic distances and revealed that these explosions were fainter than expected in a decelerating universe, indicating greater distances due to accelerated . Subsequent analyses refined these findings, estimating the universe's matter density parameter ΩM≈0.3\Omega_M \approx 0.3 and density parameter ΩΛ≈0.7\Omega_\Lambda \approx 0.7, consistent with a flat where constitutes roughly 68% of the total energy budget. This has been robustly confirmed by multiple independent probes, including the (CMB) anisotropies measured by the Planck satellite, which support a Λ\LambdaCDM model with accelerating expansion driven by a cosmological constant-like . in galaxy surveys and the integrated Sachs-Wolfe effect in CMB data further corroborate the , ruling out alternative explanations like evolving or measurement errors at high confidence levels. The implications extend to the universe's ultimate fate; in the standard Λ\LambdaCDM model, continued leads to a "Big Freeze" where galaxies recede beyond observable horizons, though ongoing tensions in expansion rate measurements (the Hubble tension) and emerging studies on dynamics, including a November 2025 suggesting the expansion may now be decelerating due to weakening , continue to refine our understanding.

Background

Historical context

In the early 20th century, theoretical foundations for an expanding emerged from applications of Albert Einstein's general theory of relativity. In 1922, Russian mathematician and physicist derived solutions to Einstein's field equations that described a dynamic capable of expansion or contraction, challenging the prevailing static model. Five years later, in 1927, Belgian priest and astronomer independently proposed a similar expanding model, suggesting that the observed recessional velocities of galaxies could be explained by space itself expanding from a "primeval atom." Empirical confirmation came in 1929 through the work of American astronomer , who analyzed the spectra of distant galaxies and established a between their —interpreted as —and distance, providing direct evidence for the 's expansion. This Hubble-Lemaître law solidified the expanding paradigm, though debates persisted in the mid-20th century between the model, which posited a finite-age evolving from a hot, dense state, and the steady-state theory, which envisioned a of constant density maintained by continuous matter creation amid expansion. The discovery of the in 1965 ultimately favored the , but the rate of expansion—whether decelerating due to —remained an open question. The recognition of accelerating expansion arrived unexpectedly in 1998, when two independent teams reported observations of distant Type Ia supernovae indicating that the universe's expansion is speeding up rather than slowing down. The High-Z Supernova Search Team, led by Adam Riess, analyzed data from 16 high-redshift supernovae and found evidence for a positive cosmological constant driving acceleration. Concurrently, the Supernova Cosmology Project, under Saul Perlmutter, examined 42 high-redshift supernovae and reached the same conclusion, suggesting that repulsive dark energy dominates the universe's dynamics. These findings, initially met with skepticism regarding systematic errors in distance measurements, were soon corroborated by additional supernova datasets and independent analyses from other groups in the late 1990s and early 2000s, firmly establishing cosmic acceleration. In acknowledgment of this paradigm shift, the 2011 Nobel Prize in Physics was awarded to Perlmutter, (a key member of the High-Z team), and Riess for their leadership in discovering the accelerating expansion of the universe.

Relation to cosmic inflation

Cosmic inflation refers to a brief period of exponential expansion in the early universe, occurring approximately between 10−3610^{-36} and 10−3210^{-32} seconds after the , driven by a hypothetical known as the inflaton. This phase rapidly increased the scale factor of the universe by a factor of at least 102610^{26}, addressing key theoretical issues in the standard model, including the horizon problem—why distant regions of the universe exhibit uniform temperatures despite never having been in causal contact—and the flatness problem—why the universe's density is so finely tuned to produce a nearly flat geometry today. The inflaton field's potential energy dominates during this epoch, leading to accelerated expansion through its negative pressure, as described in the original formulation of the theory. Following , the undergoes reheating, where the decays into particles, transitioning to a radiation-dominated characterized by decelerating expansion. This deceleration persists through the subsequent matter-dominated phase, lasting until approximately redshift z≈0.67z \approx 0.67, or about 5–6 billion years ago, when the current phase of accelerating expansion begins. In the standard Λ\LambdaCDM model, this late-time transition occurs as the energy density of overtakes that of , altering the 's dynamics from deceleration to acceleration. Unlike the early inflationary epoch, this later acceleration is a classical phenomenon observed in the present-day , distinct in both timescale and physical origin. Both cosmic and the late-time accelerating expansion share a fundamental similarity: they are driven by components with negative pressure in the , leading to an acceleration parameter q<0q < 0. For inflation, the inflaton field's equation of state w≈−1w \approx -1 mimics a cosmological constant during the slow-roll phase, while late-time acceleration is attributed to dark energy with w≤−1/3w \leq -1/3. However, key differences distinguish the two: inflation is a quantum field theory process rooted in high-energy physics, resolving early-universe paradoxes through exponential growth on microscopic scales, whereas the current acceleration is a low-energy, classical effect linked to the cosmological constant or dynamical dark energy, influencing the large-scale evolution without addressing primordial issues. Inflation also plays a crucial role in establishing the initial conditions for the universe's large-scale structure, which later observations of the accelerating expansion help probe. Quantum fluctuations in the inflaton field during inflation are amplified to super-horizon scales, seeding the density perturbations that evolve into galaxies and clusters in the post-inflationary universe. These primordial inhomogeneities, with a nearly scale-invariant spectrum, provide the foundation for structure formation that interacts with dark energy's effects in the late universe, linking early and late cosmic epochs through consistent cosmological models.

Technical definition

The accelerating expansion of the universe is characterized by a positive second time derivative of the scale factor, a¨>0\ddot{a} > 0, where a(t)a(t) describes the relative size of the universe as a function of tt in the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. This metric assumes spatial homogeneity and and takes the form ds2=−c2dt2+a2(t)[dr21−κr2+r2(dθ2+sin⁡2θ dϕ2)],ds^2 = -c^2 dt^2 + a^2(t) \left[ \frac{dr^2}{1 - \kappa r^2} + r^2 (d\theta^2 + \sin^2\theta \, d\phi^2) \right], where cc is the , κ\kappa is the spatial curvature parameter (κ=0,+1,−1\kappa = 0, +1, -1 for flat, closed, or open geometries, respectively), and the coordinates are comoving. The dynamics of a(t)a(t) are governed by the Friedmann equations, derived from Einstein's field equations applied to the FLRW metric. The first Friedmann equation relates the Hubble parameter H=a˙/aH = \dot{a}/a to the total energy density ρ\rho, curvature, and cosmological constant Λ\Lambda: H2=(a˙a)2=8πG3ρ−κc2a2+Λ3,H^2 = \left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G}{3} \rho - \frac{\kappa c^2}{a^2} + \frac{\Lambda}{3}, where GG is the gravitational constant. The second Friedmann equation, known as the acceleration equation, determines the sign of a¨\ddot{a}: a¨a=−4πG3(ρ+3pc2)+Λ3,\frac{\ddot{a}}{a} = -\frac{4\pi G}{3} \left( \rho + \frac{3p}{c^2} \right) + \frac{\Lambda}{3}, with pp the isotropic pressure associated with ρ\rho. Acceleration (a¨>0\ddot{a} > 0) requires the right-hand side to be positive, which occurs when the effective equation-of-state parameter w=p/(ρc2)w = p/(\rho c^2) satisfies w<−1/3w < -1/3 on average, implying a dominance of components with negative pressure. A key dimensionless measure of this dynamics is the deceleration parameter, q=−a¨aa˙2=12∑iΩi(1+3wi),q = -\frac{\ddot{a} a}{\dot{a}^2} = \frac{1}{2} \sum_i \Omega_i (1 + 3 w_i), where the sum is over cosmic components (e.g., matter, radiation, dark energy), Ωi=8πGρi/(3H2)\Omega_i = 8\pi G \rho_i / (3 H^2) are the present-day density parameters, and wiw_i are the corresponding equation-of-state parameters. For accelerating expansion, q<0q < 0. In the standard Λ\LambdaCDM model, the present-day value is q0≈−0.55q_0 \approx -0.55. The expansion history is often parameterized by the redshift zz, defined as z=a0a−1,z = \frac{a_0}{a} - 1, where a0a_0 is the present-day scale factor (typically normalized to 1); zz thus quantifies the lookback time to emission events, with higher zz corresponding to earlier epochs.

Observational evidence

Type Ia supernova observations

Type Ia supernovae serve as standardizable candles for cosmological distance measurements because they result from the thermonuclear explosion of a carbon-oxygen white dwarf that accretes mass from a companion until reaching the Chandrasekhar mass limit of approximately 1.4 solar masses, yielding a consistent peak absolute magnitude of around -19.3 in the B-band after standardization. This uniformity in intrinsic brightness arises from the fixed fuel mass at the Chandrasekhar limit, allowing astronomers to infer distances by comparing observed flux to this known luminosity. Pioneering observations in 1998 revealed that high-redshift Type Ia supernovae, at redshifts z ≈ 0.3–1 (corresponding to lookback times of about 4–7 billion years), appeared dimmer than predicted by models assuming a decelerating universe dominated by matter. These findings, from the High-Z Supernova Search Team (16 high-z supernovae) and the Supernova Cosmology Project (initially 42 high-z supernovae), indicated that the supernovae were farther away than expected, implying an accelerating expansion driven by a positive cosmological constant or . Combined analyses of these datasets yielded estimates of Ω_Λ ≈ 0.7 and Ω_m ≈ 0.3, favoring a flat universe with acceleration. Distances to these supernovae are derived from the luminosity distance, defined as dL=(1+z)∫0zc dz′H(z′),d_L = (1 + z) \int_0^z \frac{c \, dz'}{H(z')}, where c is the speed of light, z is the redshift, and H(z) is the Hubble parameter at redshift z. By plotting apparent magnitude against redshift and comparing to theoretical curves for different cosmological models, researchers found that accelerating models better fit the data, as the observed magnitudes were fainter (higher) than in decelerating scenarios for the same redshift. To achieve the required precision (scatter of ~0.15 mag after corrections), light curves are standardized using the Phillips relation, which correlates peak luminosity with the stretch factor s (wider light curves indicate brighter peaks, with ΔM_B ≈ -2.5(s - 1) mag). Additionally, corrections account for interstellar dust extinction via color excess measurements, assuming a Milky Way-like extinction law (R_V = 3.1). Despite these advances, limitations persist, including potential Malmquist bias, where magnitude-limited surveys preferentially detect intrinsically brighter supernovae at higher redshifts, potentially skewing distance estimates if not fully corrected. Furthermore, possible evolution in progenitor systems—such as variations in metallicity or companion type over cosmic time—could subtly alter light curve properties or luminosities, though current data show no strong evidence for such changes at z < 1.

Baryon acoustic oscillations

Baryon acoustic oscillations (BAO) arise from pressure-driven acoustic waves in the early universe's photon-baryon plasma, prior to recombination at redshift z≈1100z \approx 1100, when photons and baryons were coupled through Thomson scattering. These waves traveled at the sound speed of the fluid, establishing a characteristic comoving scale known as the sound horizon rsr_s, which froze in place at recombination as the plasma decoupled and the universe became neutral; this scale is approximately 147 Mpc in standard cosmology. The sound horizon serves as a cosmic standard ruler, imprinted on the distribution of matter and preserved in the large-scale structure of the universe, allowing measurements of cosmic distances independent of the expansion history. In galaxy surveys, the BAO signature manifests as a broad peak in the two-point correlation function at a comoving separation of roughly 105 h−1h^{-1} Mpc, corresponding to the sound horizon projected along the line of sight. Observationally, this feature is detected through the angular scale θ=rs/dA(z)\theta = r_s / d_A(z), where dA(z)d_A(z) is the angular diameter distance at redshift zz, providing a direct probe of transverse cosmic expansion; the radial counterpart involves the Hubble parameter H(z)H(z), enabling full reconstruction of the distance-redshift relation. The first robust detections of this peak occurred in the early 2000s, with the (SDSS) luminous red galaxy sample confirming the feature at 4σ significance in 2005, followed by the 6dF Galaxy Survey's measurement at low redshift (zeff=0.106z_{\rm eff} = 0.106) yielding a volume-averaged distance DV=456±27D_V = 456 \pm 27 Mpc at 5.9% precision. Subsequent surveys, including ongoing SDSS extensions like BOSS and eBOSS, have refined these detections to percent-level accuracy. BAO measurements employ the Alcock-Paczyński test to assess the isotropy of expansion by comparing radial and transverse BAO scales, which distort differently under anisotropic cosmologies; consistency with observed near-isotropy supports homogeneous, isotropic models like the Friedmann-Lemaître-Robertson-Walker metric. These data robustly constrain the flat ΛCDM model, favoring a matter density Ωm≈0.3\Omega_m \approx 0.3 and a cosmological constant driving late-time acceleration, with no significant deviations from general relativity on large scales. For instance, the 2024 Dark Energy Spectroscopic Instrument (DESI) BAO results from over 6 million galaxies and quasars deliver 1-2% precision on H(z)H(z) and dA(z)d_A(z) (or equivalently DM(z)D_M(z)), confirming accelerated expansion consistent with w=−1w = -1 to within 1σ in flat ΛCDM. By spanning redshifts from z=0z = 0 to z=3z = 3, BAO observations map the evolution of the expansion rate H(z)H(z), tracing the transition from matter-dominated deceleration to dark energy-dominated acceleration around z≈0.7z \approx 0.7; this redshift coverage complements luminosity-based probes by leveraging clustering statistics as a geometric ruler. DESI's multi-tracer approach, combining luminous red galaxies, emission-line galaxies, and quasars, achieves sub-percent isotropic precision in key bins, tightening constraints on the acceleration epoch and ruling out purely decelerating models at high significance.

Cosmic microwave background

The cosmic microwave background (CMB) provides integrated evidence for the accelerating expansion of the universe through precise measurements of its temperature and polarization anisotropies, which constrain key cosmological parameters in the standard Λ\LambdaCDM model. Observations from the Planck satellite, spanning data releases from 2013 to 2018, utilize the angular power spectra of CMB temperature (TTTT) and polarization (EEEE, TETE) to tightly bound baryon and matter densities, specifically Ωbh2=0.0224±0.0001\Omega_b h^2 = 0.0224 \pm 0.0001 and Ωmh2=0.143±0.001\Omega_m h^2 = 0.143 \pm 0.001, where h≈0.674h \approx 0.674 is the reduced Hubble constant. These constraints, combined with the assumption of spatial flatness, imply a dark energy density parameter ΩΛ≈0.68\Omega_\Lambda \approx 0.68, indicating that dark energy dominates the late-time energy budget and drives cosmic acceleration. A distinctive signature of late-time acceleration appears in the integrated Sachs-Wolfe (ISW) effect, where photons from the CMB experience a net blueshift as they traverse evolving gravitational potentials that decay due to the dominance of . This effect preferentially boosts power in the low-multipole moments (ℓ<20\ell < 20) of the CMB temperature spectrum, as the potentials deepen during matter domination but shallow afterward in an accelerating universe. Planck 2015 analyses, cross-correlating CMB maps with large-scale structure tracers like galaxy surveys, detect the ISW signal at approximately 4σ\sigma significance, providing direct evidence for ΩΛ>0\Omega_\Lambda > 0 at greater than 3σ\sigma and constraining the dark energy equation-of-state parameter w≈−1.01w \approx -1.01. Updated Planck 2018 lensing data further supports this by offering the first CMB-only detection of through the non-zero lensing potential. The angular scale of the CMB acoustic peaks also encodes information about late-time , as alters the to the last surface. The first acoustic peak, corresponding to the sound horizon at recombination, is observed at multipole ℓ≈220\ell \approx 220 with 0.03% precision in Planck data, which robustly sets the universe's flatness (Ωk≈0\Omega_k \approx 0) and is consistent with Λ\LambdaCDM predictions only if modifies the post-recombination expansion history. Without , the peaks would shift to higher ℓ\ell due to a slower late-time expansion. Likelihood analyses of Planck CMB data alone favor a negative q0<0q_0 < 0 at more than 3σ\sigma confidence, signifying current ; when combined with other probes, the Λ\LambdaCDM model provides the best fit with ΩΛ=0.685±0.007\Omega_\Lambda = 0.685 \pm 0.007. Planck 2018 delivers high-precision constraints, including H0=67.4±0.5H_0 = 67.4 \pm 0.5 km/s/Mpc, which, alongside Ωm≈0.315\Omega_m \approx 0.315, implies an acceleration epoch beginning around redshift z≈0.6z \approx 0.6 and a present-day expansion rate dominated by dark energy.

Galaxy clusters and large-scale structure

The growth of cosmic structures provides a key probe of the universe's expansion history, as the rate at which density perturbations evolve is sensitive to the balance between gravitational attraction and cosmic acceleration. In a matter-dominated universe without acceleration, the linear growth factor D(a)D(a), which describes the evolution of density perturbations with scale factor aa, scales as D(a)∝aD(a) \propto a, leading to a growth rate parameter f=dln⁡Ddln⁡a=1f = \frac{d \ln D}{d \ln a} = 1. However, in an accelerating universe dominated by dark energy, this growth is suppressed at late times, resulting in f<1f < 1. A widely used approximation for the growth rate in Λ\LambdaCDM models is f≈Ωm0.55f \approx \Omega_m^{0.55}, where Ωm\Omega_m is the present-day matter density parameter, typically yielding f≈0.5f \approx 0.5 today. This suppression manifests in the abundance of massive galaxy clusters, which form at the high-mass end of the cosmic density field and are thus highly sensitive to the growth history. Observations of cluster counts using the Sunyaev-Zel'dovich (SZ) effect, which detects the inverse Compton scattering of cosmic microwave background photons by hot intracluster gas, reveal fewer massive clusters at high redshifts than predicted in decelerating models without dark energy. Surveys such as the Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT) have identified hundreds of clusters out to z∼1.5z \sim 1.5, with abundance measurements constraining σ8(Ωm/0.27)0.3≈0.78\sigma_8 (\Omega_m / 0.27)^{0.3} \approx 0.78, favoring a low matter density and accelerating expansion consistent with Λ\LambdaCDM. Earlier optical catalogs like the Abell clusters provided initial hints of this suppression, but SZ surveys offer a more complete, mass-selected sample less biased by selection effects. Weak gravitational lensing, particularly through cosmic shear measurements of coherent galaxy shape distortions, further tests structure growth by mapping the projected matter distribution. Surveys like the (DES) and Kilo-Degree Survey (KiDS) have measured the shear power spectrum, yielding constraints on the amplitude of matter fluctuations that imply Ωm<0.4\Omega_m < 0.4. For instance, DES Year 1 results report S8≡σ8(Ωm/0.3)0.5=0.65±0.04S_8 \equiv \sigma_8 (\Omega_m / 0.3)^{0.5} = 0.65 \pm 0.04, while KiDS-1000 provides S8=0.766−0.020+0.021S_8 = 0.766^{+0.021}_{-0.020}, both supporting a low Ωm≈0.3\Omega_m \approx 0.3 and the late-time suppression expected in an accelerating universe. Redshift-space distortions (RSD) in galaxy clustering offer an additional direct measure of the growth rate, as peculiar velocities induced by gravity distort observed redshifts along the line of sight. Parameterized by fσ8f \sigma_8, where σ8\sigma_8 is the rms density fluctuation on 8 h−1h^{-1} Mpc scales, RSD measurements from early surveys like the 2dF Galaxy Redshift Survey (2dFGRS) at z≈0.15z \approx 0.15 yield fσ8≈0.45f \sigma_8 \approx 0.45, while Baryon Oscillation Spectroscopic Survey (BOSS) data up to z≈0.7z \approx 0.7 report values such as fσ8(z=0.57)=0.426±0.024f \sigma_8 (z=0.57) = 0.426 \pm 0.024, all consistent with Λ\LambdaCDM predictions for an accelerating universe with Ωm≈0.3\Omega_m \approx 0.3. Finally, the observed age of the universe aligns with these growth constraints, as acceleration allows more time for structure formation compared to a decelerating Einstein-de Sitter model. In Λ\LambdaCDM, the current age is t0≈13.8t_0 \approx 13.8 Gyr, which matches the inferred ages of the oldest globular clusters (around 12-13 Gyr) and stars, avoiding the tension that would arise in models without late-time acceleration.

Recent measurements and debates

Recent measurements in the 2020s have intensified debates surrounding the accelerating expansion of the universe, particularly through the persistent Hubble tension, which pits local determinations of the Hubble constant H0H_0 against those inferred from the cosmic microwave background (CMB). The SH0ES team, using Cepheid variables and Type Ia supernovae, reports a local H0≈73H_0 \approx 73 km/s/Mpc, while the Planck CMB analysis yields H0≈67.4H_0 \approx 67.4 km/s/Mpc; this 5σ\sigma discrepancy may signal new physics affecting the rate of cosmic acceleration. In 2024, James Webb Space Telescope (JWST) observations confirmed the SH0ES value at H0=72.6±2.0H_0 = 72.6 \pm 2.0 km/s/Mpc by independently measuring Cepheid distances in host galaxies of supernovae, reinforcing the tension without resolving it. The Dark Energy Spectroscopic Instrument (DESI) 2024 baryon acoustic oscillation (BAO) results, derived from over 6 million galaxies and quasars spanning redshifts up to z≈3.5z \approx 3.5, provide hints of evolving dark energy with equation-of-state parameter w≠−1w \neq -1, suggesting a weakening of the acceleration over cosmic time. Subsequent 2025 analyses of DESI data combined with supernova and CMB observations further indicate that dynamical dark energy models better fit the data than a constant cosmological constant, potentially implying a transition toward slower expansion in the recent universe. Meanwhile, JWST's 2024–2025 Cepheid calibrations, incorporating tip-of-the-red-giant-branch distances, refined H0H_0 to 70.4±1.970.4 \pm 1.9 km/s/Mpc when combined with Hubble Space Telescope data, bridging the gap somewhat but still highlighting unresolved tensions in acceleration measurements. Gravitational waves offer an independent probe via standard sirens, where binary neutron star mergers provide luminosity distances without relying on cosmic distance ladders. The LIGO/Virgo detection of GW170817 in 2017, associated with a kilonova counterpart, measured H0≈70−8+12H_0 \approx 70^{+12}_{-8} km/s/Mpc, consistent with local acceleration estimates; subsequent events from the third observing run have tightened constraints around 70 km/s/Mpc, supporting ongoing expansion but not fully alleviating the Hubble tension. A controversial November 2025 study from Yonsei University reanalyzed Type Ia supernova data, correcting for progenitor age biases, and combined it with BAO and CMB measurements to derive a present-day deceleration parameter q0>0q_0 > 0, implying the universe has already transitioned to deceleration with evolving that no longer drives acceleration. This result challenges the standard Λ\LambdaCDM model and has sparked debate, as it contrasts with prior evidence for persistent acceleration, though critics argue the corrections may overemphasize low-redshift effects. Upcoming missions promise clearer resolution to these debates. The Euclid telescope, having released early data in 2024–2025, is expected to map billions of galaxies for precise BAO and weak lensing measurements of dark energy evolution by the late 2020s. Similarly, NASA's Nancy Grace Roman Space Telescope, slated for launch in 2027, will survey vast sky areas to probe acceleration via supernova distances and galaxy clustering, potentially distinguishing constant from dynamic dark energy.

Explanatory models

Dark energy and the cosmological constant

In the standard ΛCDM model, the accelerating expansion of the universe is attributed to a , denoted as Λ, which appears in the as an additive term proportional to the , Rμν−12Rgμν+Λgμν=8πGc4TμνR_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}. This constant represents a uniform density, ρ_Λ, that remains invariant over time and space, corresponding to an parameter w = -1, where the pressure p = wρ c² yields negative pressure that drives repulsion. Einstein originally introduced Λ in 1917 to construct a model, but later abandoned it as his "biggest blunder" after Edwin Hubble's 1929 observations revealed cosmic expansion. The term was reintroduced in the late 1990s following evidence from observations that the universe's expansion is accelerating, positioning Λ as the simplest explanation for this phenomenon within . In the present epoch, the for the is Ω_Λ ≈ 0.69, making it the dominant component of the 's energy budget, while the is Ω_m ≈ 0.31, encompassing ordinary and . This dominance implies that , modeled as Λ, increasingly influences the 's dynamics as dilutes with expansion. Measurements of the (CMB) indicate a spatially flat , with the total Ω_total = 1 within observational uncertainties, necessitating Λ to balance the contributions from and to achieve this flatness. Despite its empirical success, the cosmological constant faces significant theoretical challenges, including the fine-tuning problem, where the observed value of ρ_Λ is extraordinarily small—about 120 orders of magnitude below the Planck scale vacuum energy expected from —requiring precise cancellation of contributions. Additionally, the coincidence problem questions why Ω_Λ and Ω_m are comparable today, despite their vastly different evolutionary histories, with matter density scaling as (1+z)^3 and Λ remaining constant. The ΛCDM model provides the best overall fit to a broad array of cosmological observations, including the power spectrum, , and large-scale structure, though it encounters tension with direct measurements of the Hubble constant (H_0).

Evolving and phantom dark energy

In models of evolving , the equation of state parameter ww varies with the scale factor aa or , allowing the dark energy density ρ\rho to change over , in contrast to the static w=−1w = -1 of a .

Quintessence

Quintessence represents a dynamical form of modeled by a canonical scalar field ϕ\phi minimally coupled to , with an associated potential V(ϕ)V(\phi) that drives the field's slow-roll . The equation of state satisfies w>−1w > -1, ensuring positive and stability, as the field's energy density decreases more slowly than during early epochs. In tracker quintessence models, the field evolves along a where its density tracks the dominant component (e.g., or ) until late times, transitioning to accelerate cosmic expansion as ϕ\phi rolls down the potential. Thawing models, conversely, begin with ϕ\phi frozen near the potential minimum before recent thawing leads to ww approaching -1 from above, consistent with observed acceleration.

Phantom Energy

Phantom energy features an w<−1w < -1, resulting in negative pressure that causes the energy density ρ\rho to increase with cosmic expansion, potentially leading to unstable dynamics. This behavior can arise from scalar fields with negative kinetic terms, known as ghost fields, which introduce instabilities like vacuum decay or tachyonic modes, though modified gravity theories may realize phantom-like effects without explicit ghosts. Observational viability requires careful tuning to avoid rapid instabilities, with constraints favoring models where ww crosses -1 transiently rather than persistently.

Big Rip Scenario

Persistent phantom energy with w<−1w < -1 can culminate in the Big Rip, where the scale factor a(t)a(t) diverges to infinity in finite proper time, shredding cosmic structures from galaxies to subatomic particles. The timescale to the Rip is estimated at approximately 22 Gyr from the present, depending on the exact ww value; for w=−1.5w = -1.5, structures disassemble sequentially over the final months. This scenario underscores the dramatic consequences of super-accelerating expansion but remains speculative, as current data limit w<−1w < -1 phases to brief epochs if present.

Parameterizations

To probe evolution, phenomenological parameterizations like the Chevallier-Polarski-Linder (CPL) model describe ww as a linear function of the scale factor: w(a)=w0+wa(1−a)w(a) = w_0 + w_a (1 - a) where w0w_0 is the present-day value and waw_a captures the change rate. The 2024 Dark Energy Spectroscopic Instrument (DESI) results, combining baryon acoustic oscillations with cosmic microwave background and supernova data, hint at w0≈−0.8w_0 \approx -0.8 and wa>0w_a > 0, suggesting dark energy weakening over time and a pivot where ww crosses -1.

2025 Implications

Recent analyses in 2025 indicate that evolving could alleviate the Hubble tension by allowing the Hubble constant H0(z)H_0(z) to decrease from local to high-redshift measurements, with reconstructed w(z)w(z) showing phantom crossings around z∼0.5z \sim 0.5 and 1.51.5. This dynamical behavior also aligns with evidence of an apparent slowdown in expansion, favoring models over Λ\LambdaCDM with Bayes factors up to ln⁡B=8.53\ln \mathcal{B} = 8.53.

Observational Constraints

Evolving dark energy models are allowed at the 2-3σ\sigma level but disfavored by combined Planck cosmic microwave background and baryon acoustic oscillation data, which yield w0=−0.904−0.033+0.034w_0 = -0.904^{+0.034}_{-0.033} (2.9σ\sigma from Λ\LambdaCDM) and stronger 3.6σ\sigma tension from BAO plus supernovae. Future surveys like DESI extensions and LSST are projected to tighten constraints to >9σ\sigma distinction from constant w=−1w = -1.

Alternative theories

Alternative theories to dark energy propose modifications to or the averaging of cosmological inhomogeneities to explain the observed accelerating expansion of the universe. These approaches aim to reproduce the effects attributed to dark energy by altering gravitational laws at cosmic scales or accounting for the universe's non-uniform structure, without introducing exotic components. While some models can fit certain datasets, they often face challenges in matching the full suite of precision observations. One prominent extension of (MOND) to relativistic cosmology is the Tensor-Vector-Scalar (TeVeS) theory, which incorporates tensor, vector, and scalar fields to modify gravity on large scales. In TeVeS, the accelerated expansion arises from adjusted gravitational dynamics rather than , allowing the theory to potentially match observations by altering how cosmic structures evolve. However, TeVeS struggles with broader cosmological consistency, such as reproducing the power spectrum. f(R) gravity theories generalize by replacing the Einstein-Hilbert action with a function of the Ricci scalar R, introducing higher-order curvature terms that can drive late-time acceleration. For instance, models like the Hu-Sawicki form incorporate parameters that yield positive acceleration in vacuum solutions while recovering on small scales. These theories explain the expansion through modified field equations, but they require screening mechanisms, such as the chameleon effect, to avoid violating solar system tests like perihelion . Backreaction effects suggest that the universe's inhomogeneities, arising from non-linear , can influence the average expansion rate, effectively mimicking without altering gravity itself. In semi-realistic models, these spatial variations over timescales of about 10 billion years contribute to an apparent by bridging discrepancies between homogeneous predictions and observations. This idea remains debated, as constraints from isotropy limit the magnitude of backreaction, indicating it cannot fully replace . Inhomogeneous models, such as the Lemaître–Tolman–Bondi (LTB) metric, posit that we reside in a large with radially varying density and Hubble rate, causing an apparent acceleration in supernova distances without global expansion speedup. These spherically symmetric setups interpret the observed dimming of distant sources as due to curved light paths in an underdense region. However, LTB models are ruled out by the of supernova data, which shows uniform expansion across sky directions, contradicting the model's inherent asymmetries. Most alternative theories, including f(R) and TeVeS, provide poorer fits to joint datasets from Type Ia supernovae and compared to the ΛCDM model. For example, analyses of the Hu-Sawicki and Starobinsky f(R) models using , , and PantheonPlus supernovae data find them consistent with at 95% confidence but with only minor evidence for deviations, often failing to fully resolve tensions without additional tuning. Despite these constraints, such theories continue to be explored to address the Hubble tension, with non-local extensions offering geometrically driven acceleration that eases discrepancies between early- and late-universe measurements.

Cosmological consequences

Future evolution of the universe

In the standard ΛCDM model, the accelerating expansion driven by a leads to eternal expansion, resulting in the heat death or Big Freeze of the universe, where matter becomes increasingly diluted and the cosmos approaches a state of maximum in an extremely cold, empty expanse over timescales exceeding 10^{100} years. This scenario implies that the universe will continue to cool as it expands indefinitely, with all physical processes grinding to a halt due to the dominance of . Key milestones in this timeline include the recession of distant galaxies beyond the observable horizon within approximately 100 billion years (10^{11} years), after which only the Local Group of galaxies remains visible due to the accelerating expansion outpacing light travel. Supermassive black holes, the longest-lived structures, will eventually evaporate via over 10^{100} years, marking the transition to a dark era dominated by photons, leptons, and radiation in just above . The accelerating expansion imposes a cosmological event horizon, limiting the observable universe to a finite comoving of about 16 billion light-years (c / H_0, with H_0 ≈ 68 km/s/Mpc), beyond which no future light signals can reach observers, even waiting an infinite time. This horizon underscores the isolation of future cosmic observers, confining their view to an ever-diminishing fraction of the universe's history. If dark energy evolves such that its equation-of-state parameter w increases above -1 in the future, the expansion could slow down, potentially leading to a recollapse or Big Crunch rather than eternal dilution. Recent analyses from the Dark Energy Spectroscopic Instrument (DESI) suggest hints of such evolution, with dark energy density possibly weakening over time, though confirmation remains pending further data. In the alternative case of phantom dark energy (w < -1), the acceleration intensifies, culminating in a Big Rip where gravitational bound structures are torn apart: galaxies disperse in about 20 billion years, solar systems in 60 million years thereafter, and atomic bonds in the final moments around 22 billion years from now.

Impact on cosmic structure formation

The accelerating expansion of the universe, driven by dark energy, suppresses the growth of cosmic structures by counteracting gravitational clustering on large scales, particularly after reionization at redshift z ≈ 6. In the standard ΛCDM model, this leads to a reduced amplitude of matter fluctuations, quantified by the parameter σ₈ ≈ 0.81 at z = 0, compared to higher values (σ₈ ≈ 1.0 or more) in an Einstein-de Sitter (EdS) universe without dark energy. This suppression becomes prominent as dark energy begins to dominate, limiting the formation of dense halos and altering the hierarchical buildup of galaxies and clusters. The transition from decelerated to accelerated expansion occurred at a redshift z ≈ 0.7, marking the when dark energy's repulsive effect overtook 's gravitational pull, halting further non-linear collapse in underdense regions and slowing the overall growth rate. Prior to this, from high s down to z ≈ 0.7, the expanded deceleratingly under domination, allowing robust ; post-transition, acceleration dilutes densities more rapidly, reducing the efficiency of mergers and accretion. This faster expansion particularly enlarges cosmic voids—underdense regions comprising much of the volume—by enhancing the separation of surrounding filaments and walls, leading to void sizes that grow disproportionately compared to denser structures. The shapes and abundances of these voids are sensitive to the equation of state, with acceleration promoting more elongated voids and influencing the large-scale filamentary network. Indirectly, this affects the history by modulating the distribution of ionizing sources in the post-reionization era, as suppressed clustering delays the buildup of galaxies capable of sustaining extended ionized bubbles. Baryonic processes, such as feedback from and active galactic nuclei (AGN), are subtly modulated by the onset of around z ≈ 0.7, as the accelerating expansion alters the timing and efficiency of gas ejection and inflow in galactic halos. While and AGN feedback dominate baryon cycling in low-mass halos (M_halo < 10^{12} M_⊙), the transition to acceleration reduces the hot gas reservoir available for cooling and , enhancing in massive systems without significantly altering overall rates. Cosmological hydrodynamical simulations like IllustrisTNG and EAGLE demonstrate the role of AGN feedback in galaxy quenching, leading to more quiescent massive galaxies at z < 1. In IllustrisTNG, the switch to kinetic-mode black hole feedback in massive halos quenches disk galaxies by expelling circumgalactic gas, matching observed red sequences. Models with evolving (w ≠ -1) introduce tensions with observations, as they predict altered structure growth that could increase galaxy merger rates at low redshifts or boost counts due to less suppression, conflicting with measured clustering amplitudes. These discrepancies highlight the need for measurements to distinguish constant from dynamic .

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