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.
A QCD-vacuum-based model of dynamical dark energy fits Planck+ACT+SPT, DESI DR2, and supernova data while reproducing the late-time evolution favored by DESI.
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.
Any background-inert λ in coincident f(Q) gravity degenerates with σ80 via an As-D0(λ) link, inflating σ80 to unphysical levels and raising As by 20-30% in tension with Planck unless fixed by As priors.
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.
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.
EMD-corrected LHC data enables a consistent CGC description of coherent and incoherent diffractive J/ψ production in γ+p and γ+Pb via Bayesian inference from combined HERA and LHC measurements.
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.
Evidence for dynamical dark energy in the w0waCDM framework is strongly dataset-dependent, driven by mismatches in low-redshift BAO distance ratios that produce divergent expansion histories and inconsistent Hubble tension relief.
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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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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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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Evolving Dark Energy Is Vacuum Energy After All
A QCD-vacuum-based model of dynamical dark energy fits Planck+ACT+SPT, DESI DR2, and supernova data while reproducing the late-time evolution favored by DESI.
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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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The Amplitude-Growth Degeneracy and Implied $A_s$ Diagnostic for Background-Inert Modified Gravity
Any background-inert λ in coincident f(Q) gravity degenerates with σ80 via an As-D0(λ) link, inflating σ80 to unphysical levels and raising As by 20-30% in tension with Planck unless fixed by As priors.
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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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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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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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Probing Dynamical Dark Energy with Late-Time Data: Evidence, Tensions, and the Limits of the $w_0w_a$CDM Framework
Evidence for dynamical dark energy in the w0waCDM framework is strongly dataset-dependent, driven by mismatches in low-redshift BAO distance ratios that produce divergent expansion histories and inconsistent Hubble tension relief.
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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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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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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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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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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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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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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.
- Exploring the interplay of late-time dynamical dark energy and new physics before recombination