Non-Gaussian estimates of tensions in cosmological parameters

Abstract

We discuss how to efficiently and reliably estimate the level of agreement and disagreement on parameter determinations from different experiments, fully taking into account non-Gaussianities in the parameter posteriors. We develop two families of scalable algorithms that allow us to perform this type of calculations in increasing number of dimensions and for different levels of tensions. One family of algorithms rely on kernel density estimates of posterior distributions while the other relies on machine learning modeling of the posterior distribution with normalizing flows. We showcase their effectiveness and accuracy with a set of benchmark examples and find both methods agree with each other and the true tension within $0.5\sigma$ in difficult cases and generally to $0.2\sigma$ or better. This allows us to study the level of internal agreement between different measurements of the clustering of cosmological structures from the Dark Energy Survey and their agreement with measurements of the Cosmic Microwave Background from the Planck satellite.

Code available at https://github.com/mraveri/tensiometer with a documented notebook at https://tensiometer.readthedocs.io/en/latest/non_gaussian_tension.html . Minor modifications wrt v1, including a new pedagogical example. Matches version accepted in PRD

References in corpus (9)

• In the Realm of the Hubble tension $-$ a Review of Solutions
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• MADE: Masked Autoencoder for Distribution Estimation
• TensorFlow Distributions
• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• Compatibility of Planck and BICEP2 in the Light of Inflation
• Internal Robustness: systematic search for systematic bias in SN Ia data
• Dark Energy Survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions
• Fully probabilistic quasar continua predictions near Lyman-α with conditional neural spline flows

Cited by in corpus (37)

• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• The $H_0$ Olympics: A fair ranking of proposed models
• The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters
• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys
• The second data release from the European Pulsar Timing Array II. Customised pulsar noise models for spatially correlated gravitational waves
• Neutrino cosmology after DESI: tightest mass upper limits, preference for the normal ordering, and tension with terrestrial observations
• Ultra-light axions and the $S_8$ tension: joint constraints from the cosmic microwave background and galaxy clustering
• Dark Energy Survey Year 3 results: cosmological constraints from the analysis of cosmic shear in harmonic space
• DES Y3 cosmic shear down to small scales: constraints on cosmology and baryons
• SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field
• Quantifying Scalar Field Dynamics with DESI 2024 Y1 BAO measurements
• Scalar field dark energy models: Current and forecast constraints
• $5\sigma$ tension between Planck cosmic microwave background and eBOSS Lyman-alpha forest and constraints on physics beyond $\Lambda$CDM
• Quantifying the tension between cosmological and terrestrial constraints on neutrino masses
• A Unified Catalog-level Reanalysis of Stage-III Cosmic Shear Surveys
• Dark Sectors with Mass Thresholds Face Cosmological Datasets
• Identifying Host Galaxies of Supermassive Black Hole Binaries Found by PTAs
• Towards a full $w$CDM map-based analysis for weak lensing surveys
• Identifying strongly lensed gravitational waves through their phase consistency
• The NANOGrav 12.5-year data set: A computationally efficient eccentric binary search pipeline and constraints on an eccentric supermassive binary candidate in 3C 66B
• The SRG/eROSITA All-Sky Survey: Weak-Lensing of eRASS1 Galaxy Clusters in KiDS-1000 and Consistency Checks with DES Y3 & HSC-Y3
• Role of the Hubble Scale in the Weak Lensing vs. CMB Tension
• Dark Energy Survey Year 3 Results: Redshift Calibration of the MagLim Lens Sample from the combination of SOMPZ and clustering and its impact on Cosmology
• Interacting dark energy constraints from the full-shape analyses of BOSS DR12 and DES Year 3 measurements
• Cosmology from Planck CMB Lensing and DESI DR1 Quasar Tomography
• Tensions in cosmology: a discussion of statistical tools to determine inconsistencies
• Growth and Geometry Split in Light of the DES-Y3 Survey
• What does a cosmological experiment really measure? Covariant posterior decomposition with normalizing flows
• Impact of weak lensing on bright standard siren analyses
• Constraining Hot Dark Matter Sub-Species with Weak Lensing and the Cosmic Microwave Background Radiation
• Efficient prescription to search for linear gravitational wave memory from hyperbolic black hole encounters and its application to the NANOGrav 12.5-year dataset
• The Indian Pulsar Timing Array Data Release 2: II. Customised Single-Pulsar Noise Analysis and Noise Budget
• Hyper Suprime-Cam Y3 results: photo-$z$ bias calibration with lensing shear ratios and cosmological constraints from cosmic shear
• Statistical consistency of sign-switching vacuum energy with cosmological observations
• Calibrating Bayesian Tension Statistics using Neural Ratio Estimation
• Dark Energy Survey Year 3 results: Cosmology with peaks using an emulator approach