Curvature tension: evidence for a closed universe

Abstract: The curvature parameter tension between Planck 2018, cosmic microwave background lensing, and baryon acoustic oscillation data is measured using the suspiciousness statistic to be 2.5 to 3$\sigma$. Conclusions regarding the spatial curvature of the universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over 50:1 against a flat universe, and over 2000:1 against an open universe.

• The paper demonstrates a 2.5-3 sigma curvature tension in combined CMB, lensing, and BAO data that supports a closed universe model.
• It employs rigorous Bayesian statistical analysis with nested sampling via CosmoChord and PolyChord to quantify model uncertainties and dataset inconsistencies.
• The analysis shows strong Bayesian odds favoring closed universe models, challenging the conventional flat universe assumption and prompting further exploration of new physics.

Overview of "Curvature tension: evidence for a closed universe" by Will Handley

The paper "Curvature tension: evidence for a closed universe" by Will Handley explores the implications of observed inconsistencies between various cosmological datasets when interpreted within the context of curved universe models. The primary focus is on the curvature tension observed between the Planck 2018 cosmic microwave background (CMB) data, CMB lensing measurements, and baryon acoustic oscillations (BAO). These tensions, being quantitatively significant, challenge the prevailing assumption of a flat universe and suggest a preference towards closed cosmological models.

Key Findings

1. Curvature Tension and Model Comparisons:
   • The paper reports a tension of about 2.5 to 3 sigma between the combined CMB, lensing, and BAO datasets when analyzed within curved universe models (denoted as $K\Lambda$CDM). This level of tension signals significant data inconsistencies.
   • Without the incorporation of CMB lensing or BAO data, the Planck 2018 dataset provides substantial Bayesian odds against a flat universe, favoring a closed universe with betting odds exceeding 50:1. Closed models are dramatically favored over open models with odds greater than 2000:1.
2. Bayesian Statistical Analysis:
   • Employing Bayesian model comparison and the suspiciousness statistic, this work rigorously quantifies tensions and model-fit probabilities among competing cosmological models.
   • Disparate prior assumptions are considered through Bayesian evidence calculations, and discrepancies in model fits are highlighted with the calculation of Kullback-Leibler divergence.
3. Inconsistencies Between Datasets:
   • The paper identifies a lack of consistency between Planck data and other measurements such as BAO, which strongly suggest a flat universe. This inconsistency is exacerbated when curvature is introduced, leading to a dissonance that cannot be reconciled with current model assumptions without questioning data integrity or exploring new physics.

Methodology

The study leverages cosmological datasets from Planck 2018 (temperature and polarization anisotropies in the CMB), Planck 2018 CMB lensing, and BOOMERANG and COBE for BAO data to perform parameter estimation and model comparison using Bayesian statistical methods. Evidence and posterior calculations utilize nested sampling algorithms via CosmoChord and PolyChord, allowing for efficient computation even in complex model spaces.

Implications and Future Directions

The paper asserts that current observations, specifically from the Planck dataset, provide a strong Bayesian indication of a closed universe and suggests reevaluation of flat cosmologies’ observational support. This finding opens possibilities for future research directions, including:

• Systematic Error Investigation: A detailed analysis of systematic errors in observational datasets and computational codes can ensure biases towards flat models do not originate from methodological artifacts.
• New Physics Exploration: Introducing curvature could potentially address both the curvature tension and the Hubble tension, hinting at necessary extensions to the $\Lambda$CDM model that incorporate additional physical phenomena.
• Theoretical Refinements: Cosmological theory may require adaptation to accommodate the inclination toward closed universes, potentially influencing the study of inflationary models and the universe's long-term behavior.

In essence, the paper presents rigorously derived evidence that challenges the cosmological community's traditional adherence to flat universe models and necessitates a consideration of alternative cosmological theories that include curvature as a variable of significant interest. This work not only provides a quantitative statistical framework for addressing cosmological tensions but also sets the stage for more comprehensive and potentially groundbreaking studies in understanding the universe's true shape and composition.