Any unified early and late dark energy scenario with a single tracking scalar field requires a potential with three distinct slopes arranged in a steep-steeper-shallow hierarchy.
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Challenges for $\Lambda$CDM: An update
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A number of challenges to the standard $\Lambda$CDM model have been emerging during the past few years as the accuracy of cosmological observations improves. In this review we discuss in a unified manner many existing signals in cosmological and astrophysical data that appear to be in some tension ($2\sigma$ or larger) with the standard $\Lambda$CDM model as specified by the Cosmological Principle, General Relativity and the Planck18 parameter values. In addition to the well-studied $5\sigma$ challenge of $\Lambda$CDM (the Hubble $H_0$ tension) and other well known tensions (the growth tension, and the lensing amplitude $A_L$ anomaly), we discuss a wide range of other less discussed less-standard signals which appear at a lower statistical significance level than the $H_0$ tension some of them known as 'curiosities' in the data) which may also constitute hints towards new physics. For example such signals include cosmic dipoles (the fine structure constant $\alpha$, velocity and quasar dipoles), CMB asymmetries, BAO Ly$\alpha$ tension, age of the Universe issues, the Lithium problem, small scale curiosities like the core-cusp and missing satellite problems, quasars Hubble diagram, oscillating short range gravity signals etc. The goal of this pedagogical review is to collectively present the current status (2022 update) of these signals and their level of significance, with emphasis on the Hubble tension and refer to recent resources where more details can be found for each signal. We also briefly discuss theoretical approaches that can potentially explain some of these signals.
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representative citing papers
First GI BAO measurement from DES Y3 photometric data yields α = 0.966 ± 0.252, consistent with density BAO α = 0.966 ± 0.037 at 0.86σ detection.
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.
A geometric invariance makes the BAO-SN Ω_m gap invariant under sound-horizon rescaling α and requires opposite w(z) deformations for the two datasets, so their combination cannot reach the local H0 value.
N-body simulations of IDE with Q=ξHρ_x show scale-dependent deviations in the matter power spectrum, density morphology, and halo abundance that standard ΛCDM-calibrated prescriptions cannot reproduce.
Model-independent reconstruction shows that early-universe modifications resolving the Hubble tension exist at the background level, requiring a smooth ~15% pre-recombination expansion rate enhancement.
Two-field axion-like early dark energy reduces Hubble tension to 1.5 sigma residual and improves high-ell CMB fits over single-field models.
Relativistic N-body simulations of Lambda_s CDM produce a redshift-dependent crest in the matter power spectrum ratio, peaking at 20-25% near the transition and leaving a 15-20% uplift at z=0 on group scales.
Under standard recombination, phantom-crossing dynamical dark energy is preferred at ~97–98.5% probability; early-time fixes to the Hubble tension erase that preference while creating severe ω_m tension with CMB.
EDE models increase inferred α_s from CMB data, strengthening tension with USR PBH models that predict negative running.
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.
Ph-Λ_sCDM realizes sign-switching dark energy via a phantom scalar on a tanh potential, enabling controlled AdS-to-dS transition without Big Rip.
Combining GWTC-4 standard sirens with TDCOSMO2025 lensing data under the distance sum rule yields H0 = 83.78 +12.53/-10.23 km/s/Mpc (13.6% precision) in one configuration, consistent with both Planck and SH0ES.
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.
A sign-switching dark energy model (Λ_s CDM) recovers positive effective neutrino masses (0.055 ± 0.050 eV) consistent with oscillation data, unlike ΛCDM which prefers negative values (-0.075 eV), for DESI DR2 + CMB + supernova fits with z_† > 2.4.
For an observer with peculiar motion, the cosmic redshift-drift signal gains a dipolar correction proportional to the flow's projected expansion, shear, and acceleration; calibrated to CF4, it is subdominant and cannot mimic an accelerating EdS universe.
Alpha-attractor quintessential inflation models are disfavored by DESI observations and Delta Neff limits from gravitational waves, as they predict an inconsistent scalar spectral index when the gravitational-wave abundance is constrained.
Tensions in the supernova intercept a_B at z~0.01 in PantheonPlus and z~0.1 in DES-Y5 point to data systematics or inter-survey inconsistencies rather than new physics, aligning H0 measurements and reducing support for dynamical dark energy.
Node-based reconstruction of cosmic expansion prefers stronger deceleration at z≈1.7 than smooth DE EoS parametrizations, isolating z~1.5-2 as a window where the latter may compress localized kinematic features permitted by current data.
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.
Galaxy cluster observations yield two preferred directions with cosmic anisotropy amplitude of about 5.3 times 10 to the minus 4 at roughly 1 sigma overall significance, though higher in the XMM-Newton subsample.
Gravitationally induced particle creation models fit cosmological data as well as ΛCDM and reduce the Hubble tension from 4.3σ to 2.4–3σ.
The w†VCDM model shows a statistically significant preference for late-time quintessence-phantom crossing dark energy, raises the Hubble constant, and satisfies neutrino mass and Neff constraints from current cosmological datasets.
Flexible dark energy equation of state parametrizations mildly favor dynamical phantom-like behavior at z~1-2, but the preference is only ~2 sigma and sensitive to the model form and extrapolation.
citing papers explorer
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Unifying Early and Late Dark Energy: Dynamical Requirements and Obstructions
Any unified early and late dark energy scenario with a single tracking scalar field requires a potential with three distinct slopes arranged in a steep-steeper-shallow hierarchy.
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Density-Shear Baryon Acoustic Oscillation as a Cosmological Consistency Check
First GI BAO measurement from DES Y3 photometric data yields α = 0.966 ± 0.252, consistent with density BAO α = 0.966 ± 0.037 at 0.86σ detection.
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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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Geometric obstruction to resolving the Hubble tension: orthogonality of scale and shape in distance measurements
A geometric invariance makes the BAO-SN Ω_m gap invariant under sound-horizon rescaling α and requires opposite w(z) deformations for the two datasets, so their combination cannot reach the local H0 value.
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Non-linear Structure Formation in Planck+DESI Favoured Interacting Dark Energy Cosmologies
N-body simulations of IDE with Q=ξHρ_x show scale-dependent deviations in the matter power spectrum, density morphology, and halo abundance that standard ΛCDM-calibrated prescriptions cannot reproduce.
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Geometric Constraints on the Pre-Recombination Expansion History from the Hubble Tension
Model-independent reconstruction shows that early-universe modifications resolving the Hubble tension exist at the background level, requiring a smooth ~15% pre-recombination expansion rate enhancement.
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Double the axions, half the tension: multi-field early dark energy eases the Hubble tension
Two-field axion-like early dark energy reduces Hubble tension to 1.5 sigma residual and improves high-ell CMB fits over single-field models.
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Nonlinear Matter Power Spectrum from relativistic $N$-body Simulations: $\Lambda_{\rm s}$CDM versus $\Lambda$CDM
Relativistic N-body simulations of Lambda_s CDM produce a redshift-dependent crest in the matter power spectrum ratio, peaking at 20-25% near the transition and leaving a 15-20% uplift at z=0 on group scales.
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Exploring the interplay of late-time dynamical dark energy and new physics before recombination
Under standard recombination, phantom-crossing dynamical dark energy is preferred at ~97–98.5% probability; early-time fixes to the Hubble tension erase that preference while creating severe ω_m tension with CMB.
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Running into tension: primordial black holes from ultra-slow-roll inflation, spectral running, and the Hubble tension
EDE models increase inferred α_s from CMB data, strengthening tension with USR PBH models that predict negative running.
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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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A Friendly Phantom: Late-time AdS-to-dS transition and cosmological tensions
Ph-Λ_sCDM realizes sign-switching dark energy via a phantom scalar on a tanh potential, enabling controlled AdS-to-dS transition without Big Rip.
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Model-independent H0 from GWTC-4 standard sirens and TDCOSMO 2025 strong lensing time delays
Combining GWTC-4 standard sirens with TDCOSMO2025 lensing data under the distance sum rule yields H0 = 83.78 +12.53/-10.23 km/s/Mpc (13.6% precision) in one configuration, consistent with both Planck and SH0ES.
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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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Negative neutrino mass or negative dark energy?
A sign-switching dark energy model (Λ_s CDM) recovers positive effective neutrino masses (0.055 ± 0.050 eV) consistent with oscillation data, unlike ΛCDM which prefers negative values (-0.075 eV), for DESI DR2 + CMB + supernova fits with z_† > 2.4.
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Expected redshift drift for tilted observers
For an observer with peculiar motion, the cosmic redshift-drift signal gains a dipolar correction proportional to the flow's projected expansion, shear, and acceleration; calibrated to CF4, it is subdominant and cannot mimic an accelerating EdS universe.
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DESI and Gravitational Wave Constraints Challenge Quintessential {\alpha}-Attractor Inflation
Alpha-attractor quintessential inflation models are disfavored by DESI observations and Delta Neff limits from gravitational waves, as they predict an inconsistent scalar spectral index when the gravitational-wave abundance is constrained.
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Cosmological intercept tension
Tensions in the supernova intercept a_B at z~0.01 in PantheonPlus and z~0.1 in DES-Y5 point to data systematics or inter-survey inconsistencies rather than new physics, aligning H0 measurements and reducing support for dynamical dark energy.
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Do equation of state parametrizations of dark energy faithfully capture the dynamics of the late universe?
Node-based reconstruction of cosmic expansion prefers stronger deceleration at z≈1.7 than smooth DE EoS parametrizations, isolating z~1.5-2 as a window where the latter may compress localized kinematic features permitted by current 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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New constraints on cosmic anisotropy from galaxy clusters using an improved dipole fitting method
Galaxy cluster observations yield two preferred directions with cosmic anisotropy amplitude of about 5.3 times 10 to the minus 4 at roughly 1 sigma overall significance, though higher in the XMM-Newton subsample.
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Revisiting the Matter Creation Process: Observational Constraints on Gravitationally Induced Dark Energy and the Hubble Tension
Gravitationally induced particle creation models fit cosmological data as well as ΛCDM and reduce the Hubble tension from 4.3σ to 2.4–3σ.
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Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity
The w†VCDM model shows a statistically significant preference for late-time quintessence-phantom crossing dark energy, raises the Hubble constant, and satisfies neutrino mass and Neff constraints from current cosmological datasets.
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Probing the sensitivity of dark energy dynamics to equation of state parametrization flexibility
Flexible dark energy equation of state parametrizations mildly favor dynamical phantom-like behavior at z~1-2, but the preference is only ~2 sigma and sensitive to the model form and extrapolation.
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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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Cosmological Viability of Exponential Infrared $f(T)$ Gravity
Exponential IR f(T) gravity Model I alleviates Hubble tension but is disfavoured by combined Planck/ACT/SPT+DESI+Pantheon+ data; Model II is ruled out because background constraints force unphysical shifts in CMB parameters.
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Unifying the Dark Sector with the New Generalized Chaplygin Gas: Observational Constraints
A generalized Chaplygin gas with redshift-dependent exponent unifies the dark sector but is statistically equivalent to ΛCDM after penalizing for extra parameters in Bayesian fits to late-time data.
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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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Resolving the Hubble Tension in the Early Dark Energy Framework with JWST and DESI Data
Axion EDE model fitted to Planck/ACT/SPT CMB, DESI BAO, and JWST UV luminosity function data yields H0 = 71.58 ± 1.05 km s^{-1} Mpc^{-1}, reduces H0 tension to 1.0 sigma, and improves Δχ^{2}_tot = -18.26 over Λ CDM.
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Geometric Matching of Local Static Regions in Cosmological Spacetimes with an Evolving Lapse
Embedding a static Schwarzschild interior into a GCT-FLRW exterior via Israel junction conditions produces a geometric consistency condition that coincides with the GCT background equations.
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On the potential for inhomogeneities to mimic an evolving dark energy
Numerical simulations show that inhomogeneities in a LambdaCDM universe can lead some observers to infer evolving dark energy parameters consistent with DESI at 2-sigma.
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Probing late-time deviations from $\Lambda$CDM with a quadratic dark energy expansion
The QDEE model fits combined cosmological datasets better than Lambda CDM, shifts the Hubble constant higher, and shows strong Bayesian evidence in its favor.
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Testing $\Lambda$CDM with ANN-Reconstructed Expansion History from Cosmic Chronometers
The ANN-reconstructed Hubble parameter H(z) from cosmic chronometers aligns with Lambda CDM predictions within uncertainties.
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Coupled Dark Energy and Dark Matter for DESI: An Effective Guide to the Phantom Divide
Coupled quintessence-dark matter models can produce an apparent phantom-crossing effective equation of state matching DESI preferences if the scalar field begins frozen in the radiation era.
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Probing cosmic anisotropy with galaxy clusters and supernovae
Analysis of galaxy cluster and supernova data reveals a ~2σ directional variation in the Hubble constant, robust across calibration methods and aligned with the CMB dipole.
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Cosmological constraints on the big bang quantum cosmology model
The JCDM model yields H0 of 66.95 plus or minus 0.51 km/s/Mpc and Omega_m of 0.3419 plus or minus 0.0065 in a flat universe, rising to H0 of 69.13 plus or minus 0.56 with slight positive curvature, fitting late-time data but struggling with full early-universe consistency.
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How Complex is Dark Energy? A Bayesian Analysis of CPL Extensions with Recent DESI BAO Measurements
Bayesian evidence from DESI BAO plus CMB and SN data favors the standard CPL evolving dark energy model over both simpler constant-w and more complex higher-order extensions.
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Crosschecking Cosmic Distances from DESI BAO and DES SNe
For DESI DR2 BAO versus DES SNe, the comoving-distance ratio is flat but the inverse-Hubble-distance ratio falls with redshift at 2.3–2.5σ, which the authors attribute to systematics.
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Beyond CPL: Evidence for dynamical dark energy in three-parameter models
Two three-parameter extensions of the mAH dark energy parametrization are compared to LambdaCDM, wCDM, CPL and others using CMB, DESI BAO, H(z), RSD and three SNIa samples, yielding Delta chi-squared improvements of 6-38 and 2-5 sigma tensions with LambdaCDM.
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Barrow holographic dark energy interacting model in the presence of radiation and matter
Numerical study of interacting Barrow holographic dark energy in non-flat universes with radiation, showing EoS transitions and higher fitted H0 values that may address Hubble tension.
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Revisiting $\Lambda$CDM extensions in light of re-analyzed CMB data
Re-analysis with PR4 Planck likelihoods reduces lensing anomaly significance and curvature preference in Lambda CDM extensions while indicating a preference for evolving dark energy consistent with DESI.
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Extended Dark Energy analysis using DESI DR2 BAO measurements
Extended analysis of DESI DR2 data confirms robust evidence for dynamical dark energy with phantom crossing preference, stable under parametric and non-parametric modeling.
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MUltiplexed Survey Telescope (MUST) Science White Paper I: Overview of Large-Scale Structure Cosmology in the Era of Stage-V Spectroscopic Surveys
MUST is a planned 6.5m Stage-V spectroscopic survey telescope targeting 100M+ galaxies and quasars to z~5.5 for large-scale structure cosmology studies.
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The Hubble tension: A decade review
Pure early or late fixes to the Hubble tension are tightly constrained; remaining options are combined early-late interacting dark energy or new physics at the local-to-homogeneous transition.
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Dissipative Cosmology and the Nature of Dark Energy: Insights from Bulk Viscosity with DESI DR2 observations
Bulk viscous fluid models for dark energy yield improved fits to supernova, BAO, and CMB data over LambdaCDM, especially in the interacting non-minimal case.
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Running Vacuum in the expanding Universe: a unified QFT paradigm for Inflation and Dark Energy
QFT in FLRW spacetime yields a running vacuum energy density ρ_vac(H) that unifies mild dynamical dark energy today with H^4 inflation without an inflaton field.
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Early- and Late-Time Modifications to $\Lambda$CDM: Implications for the Hubble Tension
An extended model with decaying dark matter around equality and w0 dark energy yields H0 ≈ 70 km/s/Mpc from Planck+ACT+DESI data, reducing Hubble tension to ~2.2σ while producing Bayesian evidence comparable to ΛCDM.
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The Quintom theory of dark energy after DESI DR2
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.
- Intertwined Constraints in Extended Cosmologies: Dark Energy, Curvature, Neutrinos, and Inflation
- Primary Constraints of Newer General Relativity