[Paper Review] Cosmology Intertwined IV: The Age of the Universe and its Curvature

Eleonora Di Valentino, Luis A. Anchordoqui+89 more|arXiv (Cornell University)|Aug 25, 2020

History and Developments in Astronomy4 citations

TL;DR

This paper investigates the age of the universe and its spatial curvature using cosmological data, focusing on tensions between early- and late-universe measurements. It finds that a slightly closed universe (Ωₖ ≈ −0.01) from Planck 2018 data increases the age to ~15.3 Gyr, potentially alleviating the H₀ tension, while stellar age estimates remain inconsistent due to model dependence, highlighting the need for improved stellar physics to resolve cosmological tensions.

ABSTRACT

A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard $Λ$ Cold Dark Matter ($Λ$CDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99\% confidence level. While new physics could be in action, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since a positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat $Λ$CDM model.

Motivation & Objective

• To assess the implications of a non-zero spatial curvature (Ωₖ) on the age of the universe and cosmological tensions.
• To evaluate the consistency between early-universe CMB data (Planck) and late-universe distance measurements (Pantheon, R19) in light of curvature.
• To investigate whether improved stellar age measurements could resolve discrepancies in H₀ and Ωₖ constraints.
• To explore how future experiments like Euclid and SKA may break degeneracies and constrain curvature to ∼10⁻³ at 95% CL.
• To examine whether curvature deviations from zero signal local inhomogeneities or true superhorizon physics in inflationary models.

Proposed method

• Uses Planck 2018 Cosmic Microwave Background (CMB) power spectra with nominal likelihood to constrain Ωₖ and H₀.
• Applies 1D posterior distributions and 68%/95% CL contour plots for Ωₖ and Aₗ to assess curvature and dark energy consistency.
• Compares CMB-derived age (tᵤ = 13.800 ± 0.024 Gyr) with stellar age estimates from globular clusters and metal-poor stars (e.g., HD 140283, 2MASS J18082002–5104378 B).
• Incorporates model-dependent stellar age uncertainties, using Gaia parallaxes and alternative fitting methods to assess scatter.
• Evaluates the impact of positive curvature on H₀ and tᵤ, showing that Ωₖ > 0 leads to tᵤ ≈ 15.31 ± 0.47 Gyr.
• Considers future constraints from CMB spectral distortions (e.g., KSZ, Compton-y) and next-gen surveys (Euclid, SKA) to probe curvature at ∼10⁻³ level.

Experimental results

Research questions

• RQ1 Can a non-zero spatial curvature resolve the H₀ tension between early- and late-universe measurements?
• RQ2 To what extent do stellar age estimates from metal-poor stars conflict with Planck-derived ages, and how does model dependence affect this?
• RQ3 What is the impact of a closed universe (Ωₖ < 0) on the predicted age of the universe and its consistency with old stars?
• RQ4 Can future experiments like Euclid and SKA break degeneracies in curvature and H₀ measurements to improve cosmological constraints?
• RQ5 Does a non-zero curvature signal local inhomogeneities or a fundamental departure from flatness in inflationary models?

Key findings

• Planck 2018 data with nominal likelihood prefer a closed universe with Ωₖ ≈ −0.01, leading to a higher age of the universe (tᵤ ≈ 15.31 ± 0.47 Gyr).
• Stellar age estimates vary significantly: HD 140283 is measured at 14.46 ± 0.8 Gyr with HST parallaxes but drops to 13.5 ± 0.7 Gyr with Gaia parallaxes.
• The age of the oldest star 2MASS J18082002–5104378 B is 13.535 ± 0.002 Gyr, but model scatter increases uncertainty to t* = 13.0 ± 0.6 Gyr.
• The anti-correlation between H₀ and tᵤ means lowering H₀ via curvature increases the age, potentially resolving the H₀ tension.
• Future surveys like Euclid and SKA may constrain Ωₖ to ∼10⁻³ at 95% CL, sufficient to test current anomalies in Planck data.
• CMB spectral distortions (e.g., KSZ, Compton-y) offer a viable method to detect curvature at levels potentially accessible to next-generation experiments.