Pantheon+ Dataset: Supernova Cosmology

• Pantheon+ is a cosmological dataset comprising 1701 rigorously cross-calibrated Type Ia supernovae over a wide redshift range for precise measurements of key cosmological parameters.
• It integrates photometric data from 18 major surveys and applies advanced light-curve modeling, calibration, and bias corrections to control systematic errors.
• The dataset underpins stringent tests of ΛCDM and alternative cosmological models, yielding percent-level constraints on H0, dark energy parameters, and cosmic expansion history.

The Pantheon+ dataset is a cosmological resource comprising the largest and most systematically cross-calibrated sample of Type Ia supernovae (SNe Ia) assembled to date. It is designed to support precision inference of fundamental cosmological parameters, including the Hubble constant ($H_0$), the matter density parameter ($\Omega_M$), and the dark energy equation-of-state parameters ($w_0$, $w_a$), while providing a detailed and rigorously constructed framework for controlling and propagating statistical and systematic uncertainties. Spanning a wide redshift range and drawing on data from numerous surveys, Pantheon+ underpins contemporary supernova cosmology and is central to addressing current tensions and uncertainties in the measurement of cosmic expansion.

1. Data Composition and Curation

The Pantheon+ sample consists of 1701 light-curve fits from 1550 unique, spectroscopically confirmed SNe Ia, covering $0.001 \leq z \leq 2.26$ (Scolnic et al., 2021, Brout et al., 2022). The compilation assimilates photometry from 18 major surveys, including low-$z$ sources (LOSS, CfA1–4, CSP, SOUSA, Foundation, CNIa0.02), intermediate-redshift (SDSS, PS1), high-redshift (SNLS, DES), and very-high-redshift (multiple HST legacy programs). Of particular note are the 42 SNe in Cepheid-host galaxies at $z<0.01$ anchoring the local distance ladder for SH0ES $H_0$ calibration (Shao et al., 22 Oct 2025).

Robustness is ensured by quality cuts on the light-curve fits (signal-to-noise, cadence, epoch coverage, fit $\chi^2$, outlier rejection). The sample includes 151 duplicate SNe (observed by multiple surveys) and 12 “SN siblings” (multiple SNe in the same host), enabling explicit internal validation of photometric calibration and intrinsic scatter corrections (Scolnic et al., 2021).

2. Calibration, Light-Curve Modeling, and Bias Corrections

Photometric calibration is achieved through the “SuperCal–Fragilistic” approach, which anchors 105 filters across all included surveys to the Pan-STARRS1 (PS1) system and ties the absolute flux scale to HST/CALSPEC primary standards. Zero-point offsets are determined with a dedicated covariance matrix, and all passbands are retrained using the SALT2–B22 model (Brout et al., 2022). The delivered data include both raw photometry and fully cross-calibrated, bias-corrected light curves in SNANA and FITS format, standardized to a reference zero-point.

Key corrections applied and modeled include:

• Milky Way extinction using the Schlegel et al. (1998) maps and Fitzpatrick (1999) extinction law.
• Host-galaxy mass step corrections, incorporated into simulations and the Tripp estimator.
• Peculiar velocity corrections for low-$z$ SNe using the 2M++ density field.

Distance moduli are computed using the conventional SALT2 “Tripp” estimator:

$$\mu = m_B + \alpha x_1 - \beta c - M - \delta_{\mathrm{bias}}(z, x_1, c, M_*) + \delta_{\mathrm{host}}(M_*)$$

where $m_B$ is the peak rest-frame $B$-band magnitude, $x_1$ the light-curve stretch, $c$ color, $M$ the nuisance absolute magnitude, $\delta_{\mathrm{bias}}$ the mean selection bias, and $\delta_{\mathrm{host}}$ the host-mass term (Scolnic et al., 2021, Brout et al., 2022).

3. Systematic Uncertainties and Covariance Matrix Construction

Pantheon+ rigorously propagates systematic uncertainties through a comprehensive covariance framework. The total covariance matrix combines:

• Statistical covariance ($C_{\rm stat}$): includes measurement errors, model fit uncertainties, peculiar velocity scatter, and lensing-induced scatter; off-diagonal terms account for duplicate SNe.
• Systematic covariance ($C_{\rm syst}$): constructed via linear-response propagation for each systematic source $S_\psi$, with terms such as photometric zeropoint errors, SALT2 model training uncertainties, Milky Way dust law, and selection bias corrections (Brout et al., 2022, Scolnic et al., 2021).

The systematic covariance is

$$C_{\rm syst}^{ij} = \sum_\psi \left( \frac{\partial \mu_i}{\partial S_\psi} \right) \left( \frac{\partial \mu_j}{\partial S_\psi} \right) \sigma_\psi^2$$

The full $1701 \times 1701$ covariance matrix is publicly released, including blocks for both statistical and systematic sources, enabling robust downstream parameter inference.

4. Cosmological Constraints and Key Results

Pantheon+ enables stringent constraints on cosmological models. When used alone, Pantheon+ yields:

• Flat $\Lambda$CDM: $\Omega_M=0.334 \pm 0.018$ (Brout et al., 2022).
• Flat $w_0$CDM: $w_0 = -0.90 \pm 0.14$ (SNe only), $w_0 = -0.978^{+0.024}_{-0.031}$ when combined with CMB and BAO (Brout et al., 2022).
• Flat $w_0w_a$CDM: $w_a = -0.1^{+0.9}_{-2.0}$ (SNe only), $w_a=-0.65^{+0.28}_{-0.32}$ with complementary datasets.

$H_0$ is determined with $$1.1\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$$ precision when combining Pantheon+ SNe with SH0ES Cepheid calibrators (Brout et al., 2022, Scolnic et al., 2021). The systematic uncertainty in $H_0$ from the SNe distance ladder comprises less than one-third of the total error budget, insufficient to resolve the Hubble tension.

Precision on dark energy parameters ($w_0$, $w_a$) reaches the $\sim3\%$ level, reflecting the constraining power of the large unbinned sample and full-covariance treatment. The inclusion of very high-redshift SNe ($z > 1$) from HST extends sensitivity to time variation in $w(z)$. Joint constraints on $H_0$ and $w$ from a uniform, consistently calibrated sample avoid cross-dataset systematics inherent in earlier compilations (Scolnic et al., 2021).

5. Statistical Consistency and Covariance Matrix Diagnostics

Analysis of the best-fit residuals reveals that the observed scatter in SN distance moduli is $\sim 7\%$ lower than predicted by the official covariance matrix, yielding a best-fit $\chi^2$ significantly below expectation (Keeley et al., 2022). This suggests an overestimation of the total variance, likely due to either:

• The addition of systematic terms as if they were uncorrelated statistical uncertainties (potential double-counting).
• Malmquist bias at high redshift reducing the observed scatter below idealized Gaussian expectations.

Subtracting an intrinsic scatter term of order $0.05$ mag from the diagonal of the covariance matrix restores statistical consistency and removes any apparent deviation from $\Lambda$CDM, even under model-independent reconstructions (Keeley et al., 2022). The effect modestly broadens parameter posteriors but does not significantly alter cosmological conclusions.

6. Applications in Testing Cosmological Models

Pantheon+ is used to test a range of cosmological frameworks:

• Varying speed of light models (meVSL): The dataset allows joint fitting of dark energy and meVSL parameters, finding mild $(1\sigma)$ indications that $c$ and $G$ were larger in the past, but evidence is not decisive in the absence of external data (Lee, 2021).
• Linearly coasting cosmology: Pure power-law expansion models ($a\propto t^\beta$) are strongly constrained, with Pantheon+ favoring $\beta = 1.33\pm0.05$, ruling out strict linear coasting ($\beta=1$) at $>6\sigma$ (Gahlaut, 2023).

Cross-validation with other probes tests the consistency and limits of various alternative and extended cosmological scenarios.

7. Inter-Dataset Consistency and Systematics

Combining Pantheon+ with other distance indicators such as BAO (DESI DR2) reveals violations of the distance duality relation $D_L = (1+z)^2 D_A$ at high significance, manifesting as a smooth, redshift-dependent offset in $D_L(z)$. The most probable sources are residual SN systematics (e.g., gray dust, calibration drift, or SN evolution), which can mimic evolving dark energy signals when left uncorrected. Implementing additional nuisance parameters to allow for duality violations restores consistency with $\Lambda$CDM ($w_0\approx-1$, $w_a\approx0$) and resolves apparent discrepancies previously interpreted as evidence for evolving dark energy (Afroz et al., 23 Apr 2025).

8. Impact, Applications, and Future Developments

Pantheon+ is foundational for precision cosmology, providing percent-level constraints on $w(z)$ and $H_0$ and supporting tests of the Cosmological Principle, such as the demonstration of uniformity in the Hubble flow at scales of $70$–$100$ Mpc (Shao et al., 22 Oct 2025). Its rigorous treatment of systematics and public release of light curves, bias-corrected magnitudes, and full covariance matrices serve as standards for future supernova cosmology analyses, including those anticipated from LSST and JWST. As cosmological constraints tighten and systematic control remains paramount, the methodologies and quality standards established in Pantheon+ will be essential for credible advances in the field.