The age of the Universe from a large sample of the oldest Galactic stars

Abstract: We estimate the age of the Universe using the Xiang & Rix sample of 247,103 Milky Way stars with high-resolution spectroscopy from LAMOST DR7 and $Gaia$ eDR3 parallaxes. Stellar ages were estimated using YY isochrones up to 20 Gyr. To remove stars with unusually high and precise ages, we require old stars to be metal-poor and $α$-enriched. We also require consistency between YY ages and those obtained with FLAME based only on $Gaia$ data. Our final sample of 155,600 stars within 5 kpc provides consistent cosmic age estimates using several techniques of increasing rigour. Our main results use an MCMC reconstruction of the latent age distribution, though our iterative reconstruction is very similar. Applying an innovative approach to our MCMC reconstruction and its uncertainties, we find that the oldest star has an age of $A_\star = 13.73^{+0.18}_{-0.15}$ Gyr. Varying the quality cuts can at most reduce this to $A_\star = 13.31^{+0.21}_{-0.18}$ Gyr or raise it to $14.02^{+0.18}_{-0.15}$ Gyr using a much lower or higher age-dependent metallicity ceiling, respectively. Our inferred $A_\star$ is consistent with the 13.6 Gyr expected in CMB-calibrated $Λ$CDM, assuming the first long-lived stars formed when the Universe was 0.2 Gyr old. This agreement casts doubt on solutions to the Hubble tension solely through new physics prior to recombination, which generally imply a cosmic age of $12.9 \pm 0.2$ Gyr to match low redshift probes. It is difficult for stellar modelling uncertainties to reconcile such a low age with our result given the low metallicities of the oldest stars in our sample and independent asteroseismic constraints.

• The paper determines a robust cosmic age of 13.73 (+0.18/–0.15) Gyr by analyzing a large sample of old Galactic subgiants.
• It employs Bayesian estimation with Yonsei-Yale isochrones, stringent quality controls, and nonparametric MCMC deconvolution to reconstruct the latent age distribution.
• The study sharpens constraints on new physics scenarios addressing the H0 tension, supporting a CMB-calibrated ΛCDM timeline.

Determining the Cosmic Age via Milky Way Oldest Stars: A Statistical Analysis

Introduction and Motivation

This paper presents a comprehensive constraints-based determination of the age of the Universe using a statistically robust sample of the oldest Galactic stars extracted from LAMOST DR7 spectra and Gaia eDR3 astrometry. The authors target over 150,000 subgiant stars, implementing Bayesian stellar age estimation (via Yonsei-Yale isochrones), applying a rigorous set of data-driven and chemical-abundance-driven quality controls, and developing novel statistical methodologies to reconstruct the underlying latent age distribution of the Milky Way’s oldest stellar populations.

A central motivation is to provide an empirical, cosmology-minimal lower bound on the Universe’s age ($A_U$), independent of early-Universe assumptions. Since the oldest observable stars closely approach the physical limit set by $A_U$, and star-formation delays ($t_f$) after the Big Bang are short and well-constrained, stellar archaeology becomes a critical cosmological observable.

This analysis is further contextualized by the ongoing Hubble constant ($H_0$) tension: late-Universe direct measurements returning $H_0$ values in $7\sigma$ conflict with early-Universe (CMB-calibrated) $\Lambda$CDM predictions. Many proposed resolutions involve changes to the high-redshift expansion rate, directly impacting the permissible age of the Universe. Thus, strong empirical lower limits on $A_U$ critically constrain possible new physics.

Data Acquisition and Quality Control

The study utilizes a sample of 247,103 Milky Way stars with precise LAMOST/DR7 spectroscopy and Gaia/eDR3 parallaxes, with age inference performed using YY isochrones capped only at 20 Gyr to minimize cosmological bias. Selection focuses on evolved subgiants to maximize age sensitivity while controlling for temperature and magnitude degeneracies.

However, the raw sample exhibits anomalous features such as nonphysical populations of stars with both extremely high ages ($A\gtrsim16$ Gyr) and small formal uncertainties—indicative of poor fits, systematic errors, or undetected binary contamination. These are mitigated via a suite of rigorous sample-level quality controls:

• Parallax accuracy: $\sigma_\varpi/\varpi<0.1$, and within 5 kpc.
• Binary and blend rejection: via Gaia $A_U$0 statistics.
• Population-driven chemical cuts: enforcement of empirically motivated [Fe/H]–age and [$A_U$1/Fe]–age relations, excluding outliers above (for [Fe/H]) or below (for [$A_U$2/Fe]) the empirical ridgelines.
• Cross-catalogue age consistency: rejection of stars with discordant YY (spectral) vs. FLAME (Gaia-based) ages, using iterative trendline outlier rejection around the empirical one-to-one locus.

The resulting “nominal” sample admits 155,600 old stars, exhibiting a physically sensible monotonic rise in age uncertainties with increasing age, and eliminating the problematic age artifacts seen in the pre-cut sample.

Extreme Value and Latent Distribution Inference

The authors employ methodologies of escalating statistical rigor to constrain the true age of the oldest Galactic stars ($A_U$3).

1. Extreme value approach: Using individual 140-point stellar age likelihoods, they assess, for a given assumed $A_U$4, the probability for the most extreme star to be observed older than $A_U$5, accounting for sample size.
2. Population prior deconvolution: They reconstruct the latent age distribution via iterative deconvolution, summing empirical age likelihoods, applying this as a prior, and iteratively updating until convergence.
3. Full MCMC-based nonparametric deconvolution: A 100-bin nonparametric model of the latent $A_U$6 is fit via MCMC, incorporating a gradient penalty to enforce smoothness and marginalizing over this hyperparameter.

The crucial diagnostic is the behavior of the tail of $A_U$7: in the absence of systematic bias, a sharp decline—or more formally, the intersection of a rapidly vanishing $A_U$8 with its MCMC-quantified uncertainty floor—denotes the empirical $A_U$9.

Main Empirical Results

The reconstructed metallicity–age tail, statistical modeling, and quality control variants consistently yield:

$t_f$0

where uncertainties are statistical conditional on the adopted sample and method. Sensitivity checks with stricter and looser chemical cuts, alternative cross-catalogue age consistency thresholds, and the removal of smoothing penalties shift $t_f$1 by no more than $t_f$2 Gyr.

A parallel analysis employing chemistry-selected, exclusively low-metallicity ($t_f$3), $t_f$4-rich stars ($t_f$5) yields compatible results, confirming the robustness of the main inference to the choice of population:

$t_f$6

Both findings are completely consistent with the CMB-predicted $t_f$7CDM star formation–adjusted expectation:

$t_f$8

assuming a conservative $t_f$9 Gyr delay for the first Population II stars.

In contrast, models resolving the $H_0$0 tension via pre-recombination new physics—especially those with a $H_0$1 uplift in $H_0$2—demand a present-day Universe at $H_0$3 Gyr, which is excluded at at least $H_0$4 even under the most extremely restrictive sample variant (with chemical cuts so aggressive they violate empirical GC and stellar ridgelines).

Theoretical and Methodological Implications

This study delivers several critical implications:

• Model-independent cosmic age constraint: The empirical lower limit from late-time fossil records is competitive in precision with CMB+BAO inferences and is essentially orthogonal, given the minimal cosmological modeling required.
• Severe restriction on early-time new physics: Any solution to the $H_0$5 tension compressing the Universe's timeline more than allowed by the observed $H_0$6 is strongly disfavored, putting pressure on models involving e.g., early dark energy or exotic pre-recombination interactions that uniformly uplift $H_0$7.
• Support for either late-time solutions or “local” effects: The data are compatible with scenarios where $H_0$8 tension arises from localized or recent departures from CMB-calibrated expansion—such as a local void or very recent dynamical modifications—since these minimally impact $H_0$9.
• Stellar model systematics are subdominant: Uncertainties in mixing length, helium enrichment ($H_0$0), and isochrone calibrations propagate to $H_0$1 transparent to the sample’s extremely low metallicity—asteroseismic measurements for ancient subgiants (see HD 140283) and the increasing leverage of large samples mitigate previous systematic floors, leaving total error dominated by data statistics and chemical selection.

Technical Innovations

Several methodological advances are noteworthy:

• Iterative, empirical population-level quality cuts: Enforcing outlier rejection in the full sample parameter space (e.g., the age–[Fe/H] plane) maximally exploits the dataset, eliminating systematic outliers invisible to naive error cuts.
• Nonparametric MCMC deconvolution: Reconstructing $H_0$2 from heteroskedastic, potentially non-Gaussian per-object age likelihoods is statistically nontrivial; the implementation allows direct connection between observed sample, parameter uncertainty, and the cosmic timeline.
• Cross-catalogue age validation: Simultaneous enforcement of multiple independent isochronic/asteroseismic pipelines sets a new benchmark for empirical reliability in stellar chronometry.

Outlook and Future Developments

Current uncertainties in $H_0$3 are at the $H_0$4 Gyr level, with comparable contributions from statistics, modeling systematics, and astrophysical delays $H_0$5. Prospects for reduction include:

• Further enlargement and homogeneity improvements in spectroscopic + astrometric old star samples (e.g., future Gaia releases, 4MOST, WEAVE).
• More systematic asteroseismic calibration for low-metallicity, old subgiants.
• Improvements in stellar evolution modeling, particularly non-solar mixture and diffusion physics, and better chemical tagging of early star formation.
• Cross-comparison with GC chronometry under consistent model assumptions, and merger history inferred from chemical/kinematic substructure.

Conclusion

The study rigorously constrains the age of the Universe via local stellar populations, arriving at $H_0$6–$H_0$7 Gyr, which robustly supports the CMB-inferred $H_0$8CDM timeline and sharply limits the parameter space for early-time solutions to the $H_0$9 tension. The methodology and results form a critical empirical benchmark for cosmological model selection, and future advances in large-sample stellar chronology will further augment the discriminatory power of local cosmic fossil records.

Reference:

"The age of the Universe from a large sample of the oldest Galactic stars" (2607.00764)