An iterative AI reasoning process proposes new dynamical dark energy equations of state that are competitive with traditional forms on supernova, BAO, and Planck data.
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Bayes in the sky: Bayesian inference and model selection in cosmology
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abstract
The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the presence of uncertainty. This trend is likely to continue in the future, when the way we collect, manipulate and analyse observations and compare them with theoretical models will assume an even more central role in cosmology. This review is an introduction to Bayesian methods in cosmology and astrophysics and recent results in the field. I first present Bayesian probability theory and its conceptual underpinnings, Bayes' Theorem and the role of priors. I discuss the problem of parameter inference and its general solution, along with numerical techniques such as Monte Carlo Markov Chain methods. I then review the theory and application of Bayesian model comparison, discussing the notions of Bayesian evidence and effective model complexity, and how to compute and interpret those quantities. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are summarized, highlighting the challenges that lie ahead.
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representative citing papers
Bayesian reconstruction and exhaustive symbolic regression on CMB, BAO, and supernova data yield the one-parameter dark energy parametrization w(a) = w0 / sqrt(a) that fits observations comparably to CPL and better than LambdaCDM.
GRAVITY+ observations yield a 12CO/13CO ratio of 91^{+24}_{-17} in β Pictoris b consistent with solar/ISM values and a tentative 1.4% atmospheric variability amplitude.
The work demonstrates that multi-tracer field-level SBI on galaxy and HI maps yields 2-7 times better constraints on Omega_m and sigma_8 than single-tracer or summary-statistic approaches, with 3D maps performing best.
Bayesian model selection over SMEFT operator subsets using a genetic algorithm and BIC approximation is applied to electroweak, Higgs, top and diboson data, finding no evidence for new physics and improved Wilson coefficient posteriors compared to global fits.
DESI DR2 BAO data exhibits 2.3 sigma tension with CMB in Lambda-CDM but prefers evolving dark energy (w0 > -1, wa < 0) at 3.1 sigma with CMB and 2.8-4.2 sigma when including supernovae.
DESI DR2 data constrain the neutrino mass sum below the inverted hierarchy minimum, yielding Bayes factor K>460 for normal hierarchy in standard cosmology.
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
Bayesian multiband analysis shows LISA and Taiji reconstruct PTA-compatible domain wall parameters in the strong-signal regime, with joint PTA priors reducing 10D degeneracies.
TOI-3664 b, TOI-4034 b, and TOI-6564 b are three newly characterized hot Jupiters around terminal-age main-sequence stars, with sub-Jupiter masses and inflated radii.
Background-inert modified-gravity couplings create a σ80–λ degeneracy under compressed CMB priors, inflating σ80 and producing spurious model preference, which an implied-A_s diagnostic exposes.
A scale-invariant model uses a diluting-matter-dependent potential to connect early and late dark energy via tunneling, alleviating the Hubble tension with best-fit early dark energy fraction ~0.3 at z~5000.
Milky Way radial and vertical dynamics are inconsistent with MOND and STVG but consistent with dark matter halos, disfavoring the former at high significance.
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.
Using combined CMB and LSS observations, the analysis sets 95% CL upper limits on oscillatory amplitudes at approximately 2% of A_s and a MAP value of 0.034 for the particle production coupling constant, finding no statistical preference for the extended models.
Intrinsic dispersion in the quasar UV/X-ray luminosity relation decreases with redshift above z~1.6 and modeling it as redshift-dependent shifts Omega_m0 by ~0.025 in flat LambdaCDM.
A QCD-vacuum dark-energy model with a two-parameter switch reproduces the DESI-preferred late-time expansion and is mildly favoured over ΛCDM by Bayesian evidence (lnB≈2.7).
New constraints on dark radiation parameters from recent cosmological datasets show the model alleviates the Hubble tension with SH0ES inclusion while remaining consistent with standard expectations without it.
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.
Factorized sequential Bayesian updates on correlated pseudo-data produce systematic deviations from the joint posterior that increase with correlation strength, while exact conditional-likelihood updates match the joint result; an information decomposition attributes the mismatch to parameter-tuned,
Bayesian evidence computation on DESI DR2 plus Planck and supernovae eliminates the frequentist 3.1 sigma preference for w0waCDM over LambdaCDM when using the DES-Dovekie recalibration, yielding ln B = -0.30 favoring the standard model.
Gravitationally induced particle creation models fit cosmological data as well as ΛCDM and reduce the Hubble tension from 4.3σ to 2.4–3σ.
Nonminimal curvature-matter coupling produces dynamical dark energy consistent with DESI observations and lunar laser ranging equivalence principle constraints.
Bayesian evidence favors a constant dark energy model for DESI plus Planck data and shows that apparent support for evolving dark energy with added supernova data stems from a 2.95 sigma tension between DESI and DES-SN5YR that the flexible model resolves.
citing papers explorer
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Physics-guided discovery of dynamical dark-energy equations of state through iterative AI reasoning
An iterative AI reasoning process proposes new dynamical dark energy equations of state that are competitive with traditional forms on supernova, BAO, and Planck data.
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Data-Driven Discovery of a Simple Phantom-Crossing Dark Energy Parametrization
Bayesian reconstruction and exhaustive symbolic regression on CMB, BAO, and supernova data yield the one-parameter dark energy parametrization w(a) = w0 / sqrt(a) that fits observations comparably to CPL and better than LambdaCDM.
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$^{13}$CO and potential variability in $\beta$ Pictoris b with GRAVITY+
GRAVITY+ observations yield a 12CO/13CO ratio of 91^{+24}_{-17} in β Pictoris b consistent with solar/ISM values and a tentative 1.4% atmospheric variability amplitude.
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Field-level multi-tracers simulation-based inference of cosmological parameters from 3D maps
The work demonstrates that multi-tracer field-level SBI on galaxy and HI maps yields 2-7 times better constraints on Omega_m and sigma_8 than single-tracer or summary-statistic approaches, with 3D maps performing best.
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Exploring the SMEFT landscape: Bayesian Model Selection for indirect discovery
Bayesian model selection over SMEFT operator subsets using a genetic algorithm and BIC approximation is applied to electroweak, Higgs, top and diboson data, finding no evidence for new physics and improved Wilson coefficient posteriors compared to global fits.
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DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints
DESI DR2 BAO data exhibits 2.3 sigma tension with CMB in Lambda-CDM but prefers evolving dark energy (w0 > -1, wa < 0) at 3.1 sigma with CMB and 2.8-4.2 sigma when including supernovae.
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From Evidence to Evident: Decisive Cosmological Evidence for the Normal Neutrino Mass Hierarchy
DESI DR2 data constrain the neutrino mass sum below the inverted hierarchy minimum, yielding Bayes factor K>460 for normal hierarchy in standard cosmology.
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The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
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PTA-Compatible Domain Walls at LISA and Taiji: Bayesian Reconstruction and Multiband Inference
Bayesian multiband analysis shows LISA and Taiji reconstruct PTA-compatible domain wall parameters in the strong-signal regime, with joint PTA priors reducing 10D degeneracies.
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TOI-3664 b, TOI-4034 b & TOI-6564 b: Three new hot Jupiters around stars approaching the terminal age main sequence
TOI-3664 b, TOI-4034 b, and TOI-6564 b are three newly characterized hot Jupiters around terminal-age main-sequence stars, with sub-Jupiter masses and inflated radii.
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The Amplitude-Growth Degeneracy and Implied $A_s$ Diagnostic for Background-Inert Modified Gravity
Background-inert modified-gravity couplings create a σ80–λ degeneracy under compressed CMB priors, inflating σ80 and producing spurious model preference, which an implied-A_s diagnostic exposes.
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Connecting Early Dark Energy to Late Dark Energy by the Diluting Matter Potential
A scale-invariant model uses a diluting-matter-dependent potential to connect early and late dark energy via tunneling, alleviating the Hubble tension with best-fit early dark energy fraction ~0.3 at z~5000.
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Milky Way Dynamics Favor Dark Matter over Modified Gravity Models
Milky Way radial and vertical dynamics are inconsistent with MOND and STVG but consistent with dark matter halos, disfavoring the former at high significance.
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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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Constraining primordial oscillations and inflationary particle production with Planck, ACT DR6, and DESI DR2
Using combined CMB and LSS observations, the analysis sets 95% CL upper limits on oscillatory amplitudes at approximately 2% of A_s and a MAP value of 0.034 for the particle production coupling constant, finding no statistical preference for the extended models.
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Redshift-Dependent Intrinsic Dispersion in the Quasar UV/X-ray Luminosity Relation
Intrinsic dispersion in the quasar UV/X-ray luminosity relation decreases with redshift above z~1.6 and modeling it as redshift-dependent shifts Omega_m0 by ~0.025 in flat LambdaCDM.
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Evolving Dark Energy Is Vacuum Energy After All
A QCD-vacuum dark-energy model with a two-parameter switch reproduces the DESI-preferred late-time expansion and is mildly favoured over ΛCDM by Bayesian evidence (lnB≈2.7).
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Exploring the Dark Sector: Interacting Radiation in Light of Modern Cosmological Probes
New constraints on dark radiation parameters from recent cosmological datasets show the model alleviates the Hubble tension with SH0ES inclusion while remaining consistent with standard expectations without it.
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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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Sequential Bayesian inference with correlated heavy-ion datasets
Factorized sequential Bayesian updates on correlated pseudo-data produce systematic deviations from the joint posterior that increase with correlation strength, while exact conditional-likelihood updates match the joint result; an information decomposition attributes the mismatch to parameter-tuned,
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The Bayesian view of DESI DR2 with unimpeded: Evidence and tension in a combined analysis with CMB and supernovae across cosmological models
Bayesian evidence computation on DESI DR2 plus Planck and supernovae eliminates the frequentist 3.1 sigma preference for w0waCDM over LambdaCDM when using the DES-Dovekie recalibration, yielding ln B = -0.30 favoring the standard model.
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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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Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model
Nonminimal curvature-matter coupling produces dynamical dark energy consistent with DESI observations and lunar laser ranging equivalence principle constraints.
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A Bayesian Perspective on Evidence for Evolving Dark Energy
Bayesian evidence favors a constant dark energy model for DESI plus Planck data and shows that apparent support for evolving dark energy with added supernova data stems from a 2.95 sigma tension between DESI and DES-SN5YR that the flexible model resolves.
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The Status of Single Scalar Field Dark Energy
Cosmological data can constrain only a handful of EFT parameters for single-scalar dark energy; extended models show modest preference over Λ but remain underdetermined and challenged by fifth forces and screening.
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RedDots: Magnetic field of the nearby active M dwarf GJ 729, and a search for companions
GJ 729 exhibits a weak, evolving large-scale magnetic field (50-145 G) and a persistent ~7 d radial velocity signal that could be a ~1.5-2 Earth-mass planet or residual stellar activity.
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Deep Learning Calibration of the Quasar X-ray/UV Luminosity Relation for Cosmological Applications
Quasar X-ray/UV luminosity relation shows non-linear redshift dependence that cannot be fixed by linear correction and requires further modeling or data screening for cosmological use.
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Signals from the early Universe: a comprehensive search for primordial features in Planck CMB datasets
Systematic re-analysis of Planck PR3 and PR4 CMB datasets finds local fit improvements of up to Δχ² ≈ -15 for certain oscillatory templates but no global significance above 2.6σ after look-elsewhere correction and Bayesian penalties.
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FR0 radio galaxy jets -- I. linking jet dynamics and high-energy emission in LEDA 55267 and LEDA 58287
3D RHD simulations of FR0 jets in LEDA 55267 and LEDA 58287 show recollimation shocks driving compactness via turbulence and deceleration, with SED modeling predicting lepto-hadronic emission at TeV energies as a testable forecast.
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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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Interacting $k$-essence field with non-pressureless Dark Matter: Cosmological Dynamics and Observational Constraints
Interacting k-essence dark energy and non-pressureless dark matter models with two interaction forms are shown to reproduce major cosmological epochs and fit observations comparably to LambdaCDM while admitting late-time de Sitter attractors.
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Interacting Scalar Fields as Dark Energy and Dark Matter in Einstein scalar Gauss Bonnet Gravity
Interacting scalar fields coupled to Gauss-Bonnet gravity yield viable dark energy and dark matter models that match Pantheon+ and DES supernova data while preferring over LambdaCDM at high redshifts with Roman mocks.
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Redshift Evolution of the HII Galaxy $L$-$\sigma$ Relation: Gaussian Process Analysis and Cosmological Implications
Bayesian model comparison using GP regression on Pantheon+ SNIa distances finds a logarithmic redshift correction to the HIIG L-σ relation statistically preferred when intrinsic dispersion is modeled, though evidence weakens without it and after Malmquist bias matching.
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Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation
A community-review taxonomy of uncertainty in physics-ML, plus validation diagnostics and toy experiments showing that no tested UQ method keeps nominal coverage outside the training domain.
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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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No evidence for phantom crossing: local goodness-of-fit improvements do not persist under global Bayesian model comparison
Global Bayesian evidence shows no statistically significant support for dynamical dark energy or phantom crossing despite limited local fit improvements in the w0wa parametrization.
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Lectures on Naturalness, String Landscape and Multiverse
Lecture notes providing a technical introduction to naturalness problems and the string theory landscape for graduate students.
- Intertwined Constraints in Extended Cosmologies: Dark Energy, Curvature, Neutrinos, and Inflation
- Revisiting the role of saturation in diffractive vector meson production
- Probing dynamical dark energy with late-time data: Evidence, tensions, and the limits of the $w_0w_a$CDM framework