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Accelerating expansion of the universe

The accelerating expansion of the universe is the observed phenomenon in which the rate of expansion of the cosmos 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.^[1]^[2] This acceleration, which followed an initial decelerating phase after the Big Bang, is primarily attributed to dark energy, a mysterious component that permeates space and is thought to have driven the universe's growth at a quickening pace.^[3] 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 recession.^[4]^[2] Subsequent analyses refined these findings, estimating the universe's matter density parameter \Omega_M \approx 0.3 and dark energy density parameter \Omega_\Lambda \approx 0.7, consistent with a flat geometry where dark energy constitutes roughly 68% of the total energy budget.^[3] This paradigm shift has been robustly confirmed by multiple independent probes, including the cosmic microwave background (CMB) anisotropies measured by the Planck satellite, which support a \LambdaCDM model with accelerating expansion driven by a cosmological constant-like dark energy.^[3] Baryon acoustic oscillations in galaxy surveys and the integrated Sachs-Wolfe effect in CMB data further corroborate the acceleration, ruling out alternative explanations like evolving dust or measurement errors at high confidence levels.^[3] The implications extend to the universe's ultimate fate; in the standard \LambdaCDM model, continued acceleration 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 dark energy dynamics, including a November 2025 analysis suggesting the expansion may now be decelerating due to weakening dark energy, continue to refine our understanding.^[3]^[5]

Background

Historical context

In the early 20th century, theoretical foundations for an expanding universe emerged from applications of Albert Einstein's general theory of relativity. In 1922, Russian mathematician and physicist Alexander Friedmann derived solutions to Einstein's field equations that described a dynamic universe capable of expansion or contraction, challenging the prevailing static model.^[6] Five years later, in 1927, Belgian priest and astronomer Georges Lemaître independently proposed a similar expanding universe model, suggesting that the observed recessional velocities of galaxies could be explained by space itself expanding from a "primeval atom."^[7] Empirical confirmation came in 1929 through the work of American astronomer Edwin Hubble, who analyzed the spectra of distant galaxies and established a linear relation between their redshift—interpreted as recessional velocity—and distance, providing direct evidence for the universe's expansion.^[8] This Hubble-Lemaître law solidified the expanding universe paradigm, though debates persisted in the mid-20th century between the Big Bang model, which posited a finite-age universe evolving from a hot, dense state, and the steady-state theory, which envisioned a universe of constant density maintained by continuous matter creation amid expansion.^[9] The discovery of the cosmic microwave background in 1965 ultimately favored the Big Bang, but the rate of expansion—whether decelerating due to gravity—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.^[10] In acknowledgment of this paradigm shift, the 2011 Nobel Prize in Physics was awarded to Perlmutter, Brian Schmidt (a key member of the High-Z team), and Riess for their leadership in discovering the accelerating expansion of the universe.^[11]

Relation to cosmic inflation

Cosmic inflation refers to a brief period of exponential expansion in the early universe, occurring approximately between $10^{-36} and $10^{-32} seconds after the Big Bang, driven by a hypothetical scalar field known as the inflaton. This phase rapidly increased the scale factor of the universe by a factor of at least $10^{26}, addressing key theoretical issues in the standard Big Bang 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 inflation, the universe undergoes reheating, where the inflaton decays into particles, transitioning to a radiation-dominated era characterized by decelerating expansion. This deceleration persists through the subsequent matter-dominated phase, lasting until approximately redshift z \approx 0.67, or about 5–6 billion years ago, when the current phase of accelerating expansion begins. In the standard \LambdaCDM model, this late-time transition occurs as the energy density of dark energy overtakes that of matter, altering the universe's dynamics from deceleration to acceleration. Unlike the early inflationary epoch, this later acceleration is a classical phenomenon observed in the present-day universe, distinct in both timescale and physical origin. Both cosmic inflation and the late-time accelerating expansion share a fundamental similarity: they are driven by components with negative pressure in the Friedmann equations, leading to an acceleration parameter q < 0. For inflation, the inflaton field's equation of state w \approx -1 mimics a cosmological constant during the slow-roll phase, while late-time acceleration is attributed to dark energy with w \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, \ddot{a} > 0, where a(t) describes the relative size of the universe as a function of cosmic time t in the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. This metric assumes spatial homogeneity and isotropy and takes the form

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 c is the speed of light, \kappa is the spatial curvature parameter (\kappa = 0, +1, -1 for flat, closed, or open geometries, respectively), and the coordinates are comoving. The dynamics of 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 = \dot{a}/a to the total energy density \rho, curvature, and cosmological constant \Lambda:

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 G is the gravitational constant. The second Friedmann equation, known as the acceleration equation, determines the sign of \ddot{a}:

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

with p the isotropic pressure associated with \rho. Acceleration (\ddot{a} > 0) requires the right-hand side to be positive, which occurs when the effective equation-of-state parameter w = p/(\rho c^2) satisfies w < -1/3 on average, implying a dominance of components with negative pressure. A key dimensionless measure of this dynamics is the deceleration parameter,

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), \Omega_i = 8\pi G \rho_i / (3 H^2) are the present-day density parameters, and w_i are the corresponding equation-of-state parameters. For accelerating expansion, q < 0. In the standard \LambdaCDM model, the present-day value is q_0 \approx -0.55. The expansion history is often parameterized by the redshift z, defined as

z = \frac{a_0}{a} - 1,

where a_0 is the present-day scale factor (typically normalized to 1); z thus quantifies the lookback time to emission events, with higher z corresponding to earlier epochs.^[12]

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.^[2] 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 dark energy.^[2] Combined analyses of these datasets yielded estimates of Ω_Λ ≈ 0.7 and Ω_m ≈ 0.3, favoring a flat universe with acceleration.^[2] Distances to these supernovae are derived from the luminosity distance, defined as

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 \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 r_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.^[13] 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^{-1} Mpc, corresponding to the sound horizon projected along the line of sight. Observationally, this feature is detected through the angular scale \theta = r_s / d_A(z), where d_A(z) is the angular diameter distance at redshift z, providing a direct probe of transverse cosmic expansion; the radial counterpart involves the Hubble parameter H(z), enabling full reconstruction of the distance-redshift relation. The first robust detections of this peak occurred in the early 2000s, with the Sloan Digital Sky Survey (SDSS) luminous red galaxy sample confirming the feature at 4σ significance in 2005, followed by the 6dF Galaxy Survey's measurement at low redshift (z_{\rm eff} = 0.106) yielding a volume-averaged distance D_V = 456 \pm 27 Mpc at 5.9% precision. ^[14] Subsequent surveys, including ongoing SDSS extensions like BOSS and eBOSS, have refined these detections to percent-level accuracy.^[15] 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.^[16] These data robustly constrain the flat ΛCDM model, favoring a matter density \Omega_m \approx 0.3 and a cosmological constant driving late-time acceleration, with no significant deviations from general relativity on large scales.^[13] 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) and d_A(z) (or equivalently D_M(z)), confirming accelerated expansion consistent with w = -1 to within 1σ in flat ΛCDM.^[13] By spanning redshifts from z = 0 to z = 3, BAO observations map the evolution of the expansion rate H(z), tracing the transition from matter-dominated deceleration to dark energy-dominated acceleration around z \approx 0.7; this redshift coverage complements luminosity-based probes by leveraging clustering statistics as a geometric ruler.^[13] 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.^[13]

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 \LambdaCDM model. Observations from the Planck satellite, spanning data releases from 2013 to 2018, utilize the angular power spectra of CMB temperature (TT) and polarization (EE, TE) to tightly bound baryon and matter densities, specifically \Omega_b h^2 = 0.0224 \pm 0.0001 and \Omega_m h^2 = 0.143 \pm 0.001, where h \approx 0.674 is the reduced Hubble constant.^[17] These constraints, combined with the assumption of spatial flatness, imply a dark energy density parameter \Omega_\Lambda \approx 0.68, indicating that dark energy dominates the late-time energy budget and drives cosmic acceleration.^[17] 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 dark energy. This effect preferentially boosts power in the low-multipole moments (\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 4\sigma significance, providing direct evidence for \Omega_\Lambda > 0 at greater than 3\sigma and constraining the dark energy equation-of-state parameter w \approx -1.01.^[18] Updated Planck 2018 lensing data further supports this by offering the first CMB-only detection of dark energy through the non-zero lensing potential.^[17] The angular scale of the CMB acoustic peaks also encodes information about late-time acceleration, as dark energy alters the angular diameter distance to the last scattering surface. The first acoustic peak, corresponding to the sound horizon at recombination, is observed at multipole \ell \approx 220 with 0.03% precision in Planck data, which robustly sets the universe's flatness (\Omega_k \approx 0) and is consistent with \LambdaCDM predictions only if acceleration modifies the post-recombination expansion history.^[17] Without dark energy, the peaks would shift to higher \ell due to a slower late-time expansion. Likelihood analyses of Planck CMB data alone favor a negative deceleration parameter q_0 < 0 at more than 3\sigma confidence, signifying current acceleration; when combined with other probes, the \LambdaCDM model provides the best fit with \Omega_\Lambda = 0.685 \pm 0.007.^[17] Planck 2018 delivers high-precision constraints, including H_0 = 67.4 \pm 0.5 km/s/Mpc, which, alongside \Omega_m \approx 0.315, implies an acceleration epoch beginning around redshift z \approx 0.6 and a present-day expansion rate dominated by dark energy.^[17]

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), which describes the evolution of density perturbations with scale factor a, scales as D(a) \propto a, leading to a growth rate parameter f = \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 < 1. A widely used approximation for the growth rate in \LambdaCDM models is f \approx \Omega_m^{0.55}, where \Omega_m is the present-day matter density parameter, typically yielding f \approx 0.5 today.^[19] 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 \sim 1.5, with abundance measurements constraining \sigma_8 (\Omega_m / 0.27)^{0.3} \approx 0.78, favoring a low matter density and accelerating expansion consistent with \LambdaCDM.^[20] 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.^[21] 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 Dark Energy Survey (DES) and Kilo-Degree Survey (KiDS) have measured the shear power spectrum, yielding constraints on the amplitude of matter fluctuations that imply \Omega_m < 0.4. For instance, DES Year 1 results report S_8 \equiv \sigma_8 (\Omega_m / 0.3)^{0.5} = 0.65 \pm 0.04, while KiDS-1000 provides S_8 = 0.766^{+0.021}_{-0.020}, both supporting a low \Omega_m \approx 0.3 and the late-time suppression expected in an accelerating universe.^[22] 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 f \sigma_8, where \sigma_8 is the rms density fluctuation on 8 h^{-1} Mpc scales, RSD measurements from early surveys like the 2dF Galaxy Redshift Survey (2dFGRS) at z \approx 0.15 yield f \sigma_8 \approx 0.45, while Baryon Oscillation Spectroscopic Survey (BOSS) data up to z \approx 0.7 report values such as f \sigma_8 (z=0.57) = 0.426 \pm 0.024, all consistent with \LambdaCDM predictions for an accelerating universe with \Omega_m \approx 0.3.^[23] 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 \LambdaCDM, the current age is t_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 H_0 against those inferred from the cosmic microwave background (CMB). The SH0ES team, using Cepheid variables and Type Ia supernovae, reports a local H_0 \approx 73 km/s/Mpc, while the Planck CMB analysis yields H_0 \approx 67.4 km/s/Mpc; this 5\sigma discrepancy may signal new physics affecting the rate of cosmic acceleration.^[24] In 2024, James Webb Space Telescope (JWST) observations confirmed the SH0ES value at H_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.^[24] 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 \approx 3.5, provide hints of evolving dark energy with equation-of-state parameter w \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.^[25] Meanwhile, JWST's 2024–2025 Cepheid calibrations, incorporating tip-of-the-red-giant-branch distances, refined H_0 to $70.4 \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 H_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.^[26] 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 q_0 > 0, implying the universe has already transitioned to deceleration with evolving dark energy that no longer drives acceleration.^[27] This result challenges the standard \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.^[28] 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.^[29]

Explanatory models

Dark energy and the cosmological constant

In the standard ΛCDM model, the accelerating expansion of the universe is attributed to a cosmological constant, denoted as Λ, which appears in the Einstein field equations as an additive term proportional to the metric tensor, R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}.^[30] This constant represents a uniform vacuum energy density, ρ_Λ, that remains invariant over time and space, corresponding to an equation of state parameter w = -1, where the pressure p = wρ c² yields negative pressure that drives repulsion.^[30] Einstein originally introduced Λ in 1917 to construct a static universe model, but later abandoned it as his "biggest blunder" after Edwin Hubble's 1929 observations revealed cosmic expansion.^[31] The term was reintroduced in the late 1990s following evidence from type Ia supernova observations that the universe's expansion is accelerating, positioning Λ as the simplest explanation for this phenomenon within general relativity.^[32] In the present epoch, the energy density parameter for the cosmological constant is Ω_Λ ≈ 0.69, making it the dominant component of the universe's energy budget, while the matter density parameter is Ω_m ≈ 0.31, encompassing ordinary and dark matter.^[33] This dominance implies that dark energy, modeled as Λ, increasingly influences the universe's dynamics as matter dilutes with expansion. Measurements of the cosmic microwave background (CMB) indicate a spatially flat universe, with the total density parameter Ω_total = 1 within observational uncertainties, necessitating Λ to balance the contributions from matter and radiation to achieve this flatness.^[33] 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 quantum field theory—requiring precise cancellation of contributions.^[34] 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.^[34] The ΛCDM model provides the best overall fit to a broad array of cosmological observations, including the CMB power spectrum, baryon acoustic oscillations, and large-scale structure, though it encounters tension with direct measurements of the Hubble constant (H_0).^[35]

Evolving and phantom dark energy

In models of evolving dark energy, the equation of state parameter w varies with the scale factor a or redshift, allowing the dark energy density \rho to change over cosmic time, in contrast to the static w = -1 of a cosmological constant.^[36]

Quintessence

Quintessence represents a dynamical form of dark energy modeled by a canonical scalar field \phi minimally coupled to gravity, with an associated potential V(\phi) that drives the field's slow-roll evolution.^[37] The equation of state satisfies w > -1, ensuring positive kinetic energy and stability, as the field's energy density decreases more slowly than matter during early epochs.^[37] In tracker quintessence models, the field evolves along a trajectory where its density tracks the dominant component (e.g., radiation or matter) until late times, transitioning to accelerate cosmic expansion as \phi rolls down the potential.^[37] Thawing models, conversely, begin with \phi frozen near the potential minimum before recent thawing leads to w approaching -1 from above, consistent with observed acceleration.^[37]

Phantom Energy

Phantom energy features an equation of state w < -1, resulting in negative pressure that causes the energy density \rho to increase with cosmic expansion, potentially leading to unstable dynamics.^[38] 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.^[39] Observational viability requires careful tuning to avoid rapid instabilities, with constraints favoring models where w crosses -1 transiently rather than persistently.^[38]

Big Rip Scenario

Persistent phantom energy with w < -1 can culminate in the Big Rip, where the scale factor a(t) diverges to infinity in finite proper time, shredding cosmic structures from galaxies to subatomic particles.^[40] The timescale to the Rip is estimated at approximately 22 Gyr from the present, depending on the exact w value; for w = -1.5, structures disassemble sequentially over the final months.^[40] This scenario underscores the dramatic consequences of super-accelerating expansion but remains speculative, as current data limit w < -1 phases to brief epochs if present.^[40]

Parameterizations

To probe evolution, phenomenological parameterizations like the Chevallier-Polarski-Linder (CPL) model describe w as a linear function of the scale factor:

w(a) = w_0 + w_a (1 - a)

where w_0 is the present-day value and w_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 w_0 \approx -0.8 and w_a > 0, suggesting dark energy weakening over time and a pivot where w crosses -1.^[41]

2025 Implications

Recent analyses in 2025 indicate that evolving dark energy could alleviate the Hubble tension by allowing the Hubble constant H_0(z) to decrease from local to high-redshift measurements, with reconstructed w(z) showing phantom crossings around z \sim 0.5 and $1.5.^[42] This dynamical behavior also aligns with evidence of an apparent slowdown in expansion, favoring models over \LambdaCDM with Bayes factors up to \ln \mathcal{B} = 8.53.^[42]

Observational Constraints

Evolving dark energy models are allowed at the 2-3\sigma level but disfavored by combined Planck cosmic microwave background and baryon acoustic oscillation data, which yield w_0 = -0.904^{+0.034}_{-0.033} (2.9\sigma from \LambdaCDM) and stronger 3.6\sigma tension from BAO plus supernovae.^[36] Future surveys like DESI extensions and LSST are projected to tighten constraints to >9\sigma distinction from constant w = -1.^[36]

Alternative theories

Alternative theories to dark energy propose modifications to general relativity 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 Modified Newtonian Dynamics (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 dark energy, allowing the theory to potentially match supernova observations by altering how cosmic structures evolve. However, TeVeS struggles with broader cosmological consistency, such as reproducing the cosmic microwave background power spectrum. f(R) gravity theories generalize general relativity 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 standard gravity 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 precession. Backreaction effects suggest that the universe's inhomogeneities, arising from non-linear structure formation, can influence the average expansion rate, effectively mimicking dark energy without altering gravity itself. In semi-realistic models, these spatial variations over timescales of about 10 billion years contribute to an apparent acceleration by bridging discrepancies between homogeneous predictions and observations. This idea remains debated, as constraints from cosmic microwave background isotropy limit the magnitude of backreaction, indicating it cannot fully replace dark energy. Inhomogeneous models, such as the Lemaître–Tolman–Bondi (LTB) metric, posit that we reside in a large local void 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 isotropy 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 baryon acoustic oscillations compared to the ΛCDM model. For example, analyses of the Hu-Sawicki and Starobinsky f(R) models using BAO, big bang nucleosynthesis, and PantheonPlus supernovae data find them consistent with general relativity 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 gravity 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 cosmological constant 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 entropy in an extremely cold, empty expanse over timescales exceeding 10^{100} years.^[43] 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 dark energy.^[43] 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.^[44] Supermassive black holes, the longest-lived structures, will eventually evaporate via Hawking radiation over 10^{100} years, marking the transition to a dark era dominated by photons, leptons, and radiation in thermal equilibrium just above absolute zero.^[43] The accelerating expansion imposes a cosmological event horizon, limiting the observable universe to a finite comoving distance 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.^[45] 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.^[46] 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.^[40]

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.^[47] 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.^[47] The transition from decelerated to accelerated expansion occurred at a redshift z ≈ 0.7, marking the epoch when dark energy's repulsive effect overtook matter's gravitational pull, halting further non-linear collapse in underdense regions and slowing the overall growth rate.^[48] Prior to this, from high redshifts down to z ≈ 0.7, the universe expanded deceleratingly under matter domination, allowing robust structure formation; post-transition, acceleration dilutes matter densities more rapidly, reducing the efficiency of mergers and accretion.^[48] 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.^[49] The shapes and abundances of these voids are sensitive to the dark energy equation of state, with acceleration promoting more elongated voids and influencing the large-scale filamentary network.^[49] Indirectly, this affects the reionization 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.^[50] Baryonic processes, such as feedback from stars and active galactic nuclei (AGN), are subtly modulated by the onset of dark energy around z ≈ 0.7, as the accelerating expansion alters the timing and efficiency of gas ejection and inflow in galactic halos.^[51] While supernova 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 star formation, enhancing quenching in massive systems without significantly altering overall star formation rates.^[51]^[52] 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.^[53] Models with evolving dark energy (w ≠ -1) introduce tensions with observations, as they predict altered structure growth that could increase galaxy merger rates at low redshifts or boost dwarf galaxy counts due to less suppression, conflicting with measured clustering amplitudes.^[47] These discrepancies highlight the need for growth factor measurements to distinguish constant from dynamic dark energy.^[47]

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