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The Cosmological Constant and Dark Energy
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Physics invites the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, Lambda; nowadays the concept is termed dark energy or quintessence. Physics also suggests the dark energy could be dynamical, allowing the arguably appealing picture that the dark energy density is evolving to its natural value, zero, and is small now because the expanding universe is old. This alleviates the classical problem of the curious energy scale of order a millielectronvolt associated with a constant Lambda. Dark energy may have been detected by recent advances in the cosmological tests. The tests establish a good scientific case for the context, in the relativistic Friedmann-Lemaitre model, including the gravitational inverse square law applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one quarter of the critical Einstein-de Sitter value. The case for detection of dark energy is serious but not yet as convincing; we await more checks that may come out of work in progress. Planned observations might be capable of detecting evolution of the dark energy density; a positive result would be a considerable stimulus to attempts to understand the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.
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Showing 60 of 83 Pith papers that cite this
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Dark Energy and Neutrino Flavor from the Weak Axion
The dark-energy scale is predicted from neutrino masses and PMNS mixing: the weak-axion Coleman-Weinberg potential lands at 1-4 meV for current neutrino data.
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$\Lambda_{\rm s}$CDM cosmology from a type-II minimally modified gravity
Λ_s VCDM is a predictive model combining Λ_s CDM with VCDM gravity via an auxiliary scalar field and sigmoid-smoothed potentials to enable stable mirror AdS-to-dS transitions with possible transient acceleration.
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Defocusing dark energy: Raychaudhuri diagnostics beyond $w<-1/3$ and the phantom divide
For sign-changing effective dark energy, smooth negative-to-positive density crossings make ρ+3p and ρ+p the correct diagnostics, give w=p/ρ a universal pole n(1+z†)/3, and force repulsion onset z_rep>z† while ρ<0.
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The unavoidable de Sitter fate of a scale-invariant Universe
Stable flat solutions in scale-invariant scalar-tensor theories carry a non-vanishing cosmological constant unless the quartic coupling vanishes, and this vanishing is not radiatively protected, making a residual CC generic.
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A solid unification of the dark sector
A generalized Chaplygin-type solid unifies dark matter and dark energy via an early pressureless phase transitioning to a late solid phase that supports acceleration and produces distinct low-redshift perturbation signatures.
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Nonminimally coupled quintessence with sign-switching interaction
A new quintessence model with non-minimal coupling produces an effective sign-switching interaction that fits current data better than LambdaCDM or w0waCDM and accounts for late-time dark energy weakening without phan...
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Revisiting observational constraints on coupled exponential quintessence with energy and momentum transfers: degeneracy with massive neutrinos
Allowing the neutrino mass to vary removes the 2σ evidence for momentum transfer between dark energy and dark matter in coupled quintessence, via a degeneracy with the energy-exchange coupling.
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Evidence for deviation in gravitational light deflection from general relativity at cosmological scales with KiDS-Legacy and CMB lensing
KiDS-Legacy weak lensing plus CMB data yields a 3 sigma deviation in light deflection from GR in a Lambda CDM background, with the signal driven by large-scale CMB lensing amplitudes.
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Realizing the phantom-divide crossing with vector and scalar fields
A scalar-vector-tensor dark-energy model crosses the phantom divide at low redshift with no ghost or Laplacian instabilities and growth signatures close to LCDM.
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Towards a unified quantum field theory of dark energy and inflation: unstable de Sitter vacuum and running vacuum
The vacuum energy of quantum fields, computed exactly in de Sitter spacetime and then allowed to decay into radiation, can drive H^4-powered inflation and leave a slowly running dark energy δρ_vac ~ m_Pl^2 H^2, unifyi...
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Quasinormal modes of nonlocal gravity black holes
Quasinormal frequencies of nonlocal gravity black holes deviate from Schwarzschild values by up to about 12%, and the derived bounds on the model parameters α and k depend on projected detector sensitivity.
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Nonlocal gravity in a proper tetrad frame: traversable wormholes
Static, spherically symmetric traversable wormholes are built in revised Deser-Woodard nonlocal gravity by reconstructing the theory's distortion function from chosen wormhole metrics.
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Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter
The paper derives eikonal quasinormal mode frequencies and shock-wave switchback delays in Schwarzschild-de Sitter for arbitrary mass, using static-sphere observers and reflecting boundary conditions.
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Inflation in non-local hybrid metric-Palatini gravity
Non-local hybrid metric-Palatini gravity generically contains ghosts, but a degenerate subclass with metric f(R) gravity plus Palatini non-local terms is ghost-free and can drive slow-roll inflation resembling Starobi...
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A comprehensive numerical study on four categories of holographic dark energy models
Seven holographic dark energy models are constrained with DESI BAO, Planck CMB, and PantheonPlus supernovae; LambdaCDM stays preferred, Ricci dark energy is ruled out, and event-horizon models show large data-set-depe...
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Apparent horizon thermodynamics in an exponential $f(Q)$ gravity model
In an exponential f(Q) model, apparent-horizon entropy gains exponentially suppressed corrections to the area law, and the generalized second law excludes parameter values b>0.26 in the future-redshift region.
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Do we really need alternatives to the $\omega_0\omega_a$CDM parameterization after the DESI DR2?
In a common physically motivated pivot basis, the standard CPL parameterization is mildly preferred over the fafbCDM density expansion and reproduces quintessence backgrounds at least as well.
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Entropic Chaplygin-Gas cosmology and late-universe tension diagnostics
An entropic Chaplygin-gas dark sector can shift fitted H0 values, but the shift and any tension relief depend on supernova calibration and vanish with DES-Dovekie data.
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Cosmological horizon thermodynamics in Gauss-Bonnet quasi-dilaton Massive Gravity
Gauss-Bonnet quasi-dilaton massive gravity is claimed to obey horizon thermodynamics and the holographic entropy bound, provided the Gauss-Bonnet coupling is non-negative.
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Gravitational wave echoes as probes of the maximum mass of strange stars in quadratic curvature-matter coupled gravity
In f(R+αR²,T) gravity with tuned parameters, MIT-bag strange stars can exceed the compactness needed for photon spheres and would produce kHz gravitational-wave echoes.
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The Goldstone Awakens: Unimodular dark energy in scale-invariant $R^2$ gravity
In a scale-invariant R² + unimodular-gravity model, the Goldstone boson of scale symmetry becomes thawing dark energy, with its equation of state fixed by the same coupling that sets the inflationary spectral tilt.
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Distance duality relation in symmetric teleparallel gravity
In symmetric teleparallel f(Q) gravity with nonminimal EM-nonmetricity coupling, the distance duality relation is dynamically violated, yielding a generalized formula relating observational distances to the Hubble rate.
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Microscopic entropy of de Sitter spacetime and entropic solution to the old cosmological constant problem
Requiring the RG flow of the de Sitter entropy parameter α to increase monotonically toward the infrared yields a cosmological constant matching the observed value.
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An Interplay Between Fractional Calculus and Holographic Dark Energy
Introduces Fractional Holographic Dark Energy (FHDE) via fractionally corrected entropy from a modified Wheeler-DeWitt equation and studies its late-time cosmology, field reconstructions, and extensions to modified gr...
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Reconstructing dark energy with fewer assumptions
Bin-wise uncorrelated reconstruction from DESI/SDSS BAO and Pantheon+/Union3.1/DES-Dovekie supernovae yields dark energy density peaking then declining and equation of state oscillating with phantom crossing near z~0....
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Signatures of Modified Gravity on Linear Scales in a Dynamical Dark Energy Background
Using Planck, DESI, supernovae, and redshift-space distortions, the authors infer that modified gravity, if present, must act only below ~30 Mpc and cannot modify the large scales previously considered.
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Constraints on Schwarzschild Black Hole in a Generalized Dehnen-Type $(1,4,\gamma)$ Dark Matter Halo via the S2 Star Orbit around Sgr A$^\star$
Derives perihelion shift equations for S2 star in generalized Schwarzschild-Dehnen BH-DM spacetime and constrains gamma, rho_s, rs via MCMC on Do et al. and Gillessen et al. datasets.
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Generalizing the CPL Parametrization through Dark Sector Interaction
Generalized interacting dark energy models with constant or dynamical couplings yield analytical density expressions but are not preferred over LambdaCDM by Bayesian evidence from DESI, Pantheon+, and CMB data.
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Measuring neutrino mass in light of ACT DR6 and DESI DR2
New ACT and DESI data yield model-dependent upper limits on sum of neutrino masses, with holographic dark energy giving the tightest bounds and a consistent preference for degenerate hierarchy.
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Statistical consistency of sign-switching vacuum energy with cosmological observations
Using exact non-Gaussian shift and posterior predictive tests, ΛsCDM improves CMB–BAO consistency and softens but does not resolve the Hubble tension, which persists at p≈4×10⁻⁴.
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Exponential Quintessence Model: Analytical Quantification of the Fine-Tuning Problem in Dark Energy
Exponential quintessence with an assumed kination epoch relaxes the dark energy fine-tuning problem by dozens of orders of magnitude relative to a cosmological constant.
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Scaling solutions in three-form cosmology
A generalized three-form dark-energy Lagrangian admits stable scaling attractors that track the dominant cosmic fluid and, via a double-potential extension, exit to late-time acceleration — physical content dual to kn...
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Hints Beyond $\Lambda$CDM from Barrow and Tsallis Holographic Dark Energy with GO cutoff
Barrow holographic dark energy with the Granda-Oliveros cutoff fits current background data as well as ΛCDM and shows a weak AIC preference only for the Union3-based dataset combination.
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Dynamical system analysis of the cosmological phases in Palatini $k$-essence gravity
Dynamical systems analysis of a Palatini k-essence model identifies fixed points for quasi-de-Sitter epochs, scaling solutions, and quintessence phases connected by heteroclinic orbits in flat FLRW cosmology.
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Exponential $f(R)$ cosmology with massive neutrinos as a dynamical dark energy framework
Exponential f(R) gravity with massive neutrinos fits current expansion data about as well as ΛCDM and yields slightly different H0 and Σmν constraints, but does not eliminate the Hubble tension.
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Probing Dark Energy Microphysics with kSZ Tomography
Fisher-matrix forecasts for LSST- and CMB-S4-like surveys show kSZ tomography tightens constraints on dark energy parameters w0 and wa by 15% and 32% while assessing detectability of perturbations for different sound speeds.
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DESI constraints on two-field quintessence with exponential potentials
A two-field exponential-potential quintessence model fits DESI+CMB+SnIa data with moderate Bayesian preference over ΛCDM and slope parameters λφ≈λχ≈1.
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Extending CSST Emulator to post-DESI era
A tuned 'spectral equivalence' mapping lets the CSST emulator predict nonlinear matter power spectra at ~1% accuracy across the DESI DR2+CMB dynamic-dark-energy posterior.
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Updated observational constraints on $\phi$CDM dynamical dark energy cosmological models
Updated φCDM constraints from Planck 2018 + non-CMB data find α=0.055±0.041, consistent with a cosmological constant and only mildly favoring evolving quintessence.
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Gauge invariant perturbations of $F(T,T_G)$ Cosmology
Derives gauge-invariant perturbation equations for F(T, T_G) cosmology and provides physical interpretations for new contributions in each mode.
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Properties of the magnetic universe with positive cosmological constant
The paper works out the geometry, flux, and geodesics of the Melvin magnetic universe with a positive cosmological constant, showing its two-sphere section is compact and carries a conical singularity, with a Freund-R...
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Cosmo-Learn: code for learning cosmology using different methods and mock data
An open-source toolkit that simulates late-universe cosmological observations and benchmarks MCMC, genetic algorithms, Gaussian processes, Bayesian ridge regression, and neural networks in one pipeline.
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Resolving the Planck-DESI tension by nonminimally coupled quintessence
Non-minimally coupled quintessence resolves the Planck-DESI Ω_m tension at >3σ while the effective equation of state stays above w=-1 and other tensions on neutrino mass and growth rate are relieved.
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How Holographic is the Dark Energy? A Spline Nodal reconstruction approach
A three-node spline reconstruction of holographic dark energy improves chi-squared over LambdaCDM by about 10 to 12, but Bayesian evidence gives no clear preference.
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Is Dark Energy an Effective Manifestation of Non-equilibrium Thermodynamics? -- Insights from DESI
Two phenomenological dark matter creation rates can reproduce the accelerated expansion of the universe and fit current background data as well as or slightly better than LambdaCDM for some DESI-based data combinations.
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Comparison of $R_h=ct$ and $\Lambda$CDM using DESI DR1 measurements
Using DESI DR1 distance measurements, flat LambdaCDM is decisively preferred over R_h=ct, driven almost entirely by the Lyman-alpha data point at redshift 2.33.
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Teleparallel dark energy in a nonflat universe
Nonflat teleparallel dark energy with a vanishing potential is statistically favored over Lambda CDM in the authors' MCMC fit and mildly prefers an open universe.
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Robustness of dark energy phenomenology across different parameterizations
The viability of minimally and non-minimally coupled quintessence models is robust across CPL, JBP, BA, and EXP parameterizations, with all four reproducing the models' predicted observables accurately.
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Correspondence between Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology
With a specific choice of connection functions, Myrzakulov F(R,Q) gravity and Tsallis cosmology produce identical background expansion but different growth of density perturbations.
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Illustrating the consequences of a misuse of $\sigma_8$ in cosmology
Cosmologists should compare clustering amplitude with the h-independent statistic sigma_12 instead of sigma_8, because sigma_8's smoothing scale shifts with H0 and artificially worsens the growth tension in high-H0 models.
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Role of internal space correlations in the dynamics of a higher-dimensional Bianchi type-I universe: shear scalar and Hubble parameter perspectives
A constant correlation between external and internal expansion rates yields exact Bianchi type-I solutions whose effective dark energy mimics a cosmological constant at late times and a steady-state universe for negat...
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Understanding curvature-matter interaction in viable $f(R)$ dark energy models: A dynamical analysis approach
In two f(R) gravity models, a specific matter-curvature interaction shifts the fixed points and can create stable late-time accelerating attractors, but the attractors appear only for parameter values outside the mode...
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Composite Dark Energy and the Cosmological Tensions
A composite dark energy with negative-energy phantom matter before z≈1.5 and quintessence afterward improves the fit over ΛCDM by ΔAIC≈60 and resolves both tensions with BAO 2D, but not with BAO 3D.
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Modified gravity from Weyl connection and the $f(R,\cal{A})$ extension
Weyl-connection gravity with a dynamical vector field produces an effective dark energy sector, recovering Lambda-CDM in one class and dynamical dark energy in others.
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Model-independent calibration of Gamma-Ray Bursts with neural networks
Neural networks calibrate 2D and 3D Dainotti relations on the Platinum GRB sample via ANN-driven MCMC to produce a model-independent Hubble diagram with reduced scatter.
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Hubble tension: a short review of theoretical explanations
A comprehensive review finds no theoretical Hubble-tension solution yet passes all consistency tests; new early-dark-energy chains reach high H0 only when the SH0ES calibration is added.
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Intertwined Constraints in Extended Cosmologies: Dark Energy, Curvature, Neutrinos, and Inflation
Dynamical dark energy remains preferred across extended models while curvature, neutrino mass and inflation parameters show strong model dependence, with no resolution of the H0 tension.
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Generalizing the interacting dilatonic ghost condensate as a dark energy model
Generalizes the interacting dilatonic ghost condensate dark energy model, performs phase-space analysis for non-interacting and two interacting cases, and reports parameter constraints from Cosmic Chronometers, Panthe...
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Kiselev black hole and the ultra-slow evaporating behavior
Lowering the quintessence state parameter w_q in Kiselev black holes produces ultra-slow evaporation distinct from PFDM and Horndeski cases, offering a possible constraint on w_q.
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Slowly rotating traversable wormholes supported by radially varying string-fluid matter: From regular geometries to photon trajectories
Derives regular, horizon-free, asymptotically flat spacetimes for slowly rotating wormholes supported by radially varying string fluids and analyzes photon trajectories and circular orbits.
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