Pantheon+ Supernova Compilation

• Pantheon+ is a comprehensive dataset of 1550 unique Type Ia supernovae, offering precise measurements to constrain cosmic expansion and dark energy.
• The compilation integrates advanced photometry, uniform SALT2 light-curve standardization, and robust systematic error mitigation across 18 surveys.
• Cosmological analyses with Pantheon+ yield tighter constraints on H₀, Ωₘ, and w while probing cosmic anisotropy and addressing calibration tensions.

The Pantheon+ supernova compilation is a cross-calibrated, high-statistics assembly of spectroscopically confirmed Type Ia supernovae (SNe Ia) designed to yield precise constraints on cosmic expansion, dark energy, and large-scale isotropy. Building on the foundation of the original Pantheon sample, the Pantheon+ program introduced methodological advances in photometry, calibration, systematic error mitigation, and statistical cross-survey integration. These enhancements collectively enable state-of-the-art measurements of cosmological parameters such as the Hubble constant (H₀), matter density (Ωₘ), and the dark energy equation-of-state (w), while also supporting rigorous investigations into the physical standardization of SNe Ia, possible cosmological anisotropies, and tensions between different cosmological probes.

1. Data Composition, Calibration, and Methodological Advances

Pantheon+ comprises 1701 light curves corresponding to 1550 unique SNe Ia, drawing on 18 distinct surveys spanning $z\approx0.001$ to $z>2.2$. A defining feature is the inclusion of a large low-redshift ($z<0.01$) subset, crucial for absolute distance calibration, especially via Cepheid host anchoring (the SH0ES program). High-redshift SNe, including those from HST (SCP/GOODS/CANDELS), extend the redshift reach and supply leverage for constraining the evolution of dark energy.

Key improvements over earlier samples include:

• Photometry: Adoption of “forced photometry” with improved PSF-fitting routines and robust seasonal image templates. Scene modeling photometry cross-checks confirm sub-millimag photometric agreement, keeping systematics subdominant (Scolnic et al., 2017, Scolnic et al., 2021).
• Astrometry: Iterative, PSF-based centroiding reduces centroid bias, with calibration for photometric bias as a function of centroid uncertainty (Scolnic et al., 2017).
• Calibration: All photometric systems are mapped to a common flux scale via an expanded “Supercal” (and subsequent “Fragilistic”) cross-calibration, exploiting the PS1 Ubercal, with cross-survey zero-point corrections at millimag precision (Scolnic et al., 2017, Brout et al., 2022).
• Light-curve Standardization: Uniform SALT2 fitting across all surveys, updated stretch ($x_1$) and color ($c$) corrections, and bias corrections ($\delta_{\mu\,\mathrm{bias}}$). Intrinsic-scatter modeling and new selection bias frameworks (e.g., BEAMS with Bias Corrections, BBC) are implemented.
• Systematic Error Budget: Construction and propagation of a full systematic covariance matrix, capturing photometric, calibration, peculiar velocity, and training model uncertainties (Scolnic et al., 2021, Brout et al., 2022).

Methodological refinements in redshift measurements, peculiar velocity corrections, and survey cross-validation with “duplicate SNe” and “SN siblings” further support robust standardization and accurate error propagation.

2. Cosmological Parameter Constraints and Robustness

Pantheon+ enables precise inference of cosmological parameters within multiple cosmological models. The canonical approach employs the Tripp relation for the SN distance modulus: $$\mu = m_B + \alpha\,x_1 - \beta\,c - M - \delta_{\mu\,\mathrm{bias}}$$ where $\mu$ is the standardized distance modulus, $m_B$ the observed peak brightness, and $M$ the fiducial SN absolute magnitude.

Key results from the Pantheon+ cosmological analysis (with and without SH0ES/other external datasets) include:

Model	Parameter	SNe-only Constraint	SNe+SH0ES/CMB/BAO
Flat ΛCDM	Ωₘ	$0.334 \pm 0.018$	–
Flat w₀CDM	$w_0$	$-0.90 \pm 0.14$	$-0.978^{+0.024}_{-0.031}$
Flat w₀wₐCDM	$w_a$	$-0.1^{+0.9}_{-2.0}$	$-0.65^{+0.28}_{-0.32}$
Hubble constant ($H_0$)		–	$73.5 \pm 1.1$ km/s/Mpc

These settings result in a factor-of-two tightening of constraints versus earlier compilations. Notably, the dark energy equation-of-state, $w$, is statistically consistent with $-1$ (cosmological constant), with no requirement for strong evolution ($w_a\sim 0.28$ after multi-probe combination) (Brout et al., 2022). The SNe-only $w_0$ is shifted slightly higher, but systematic uncertainties are fully included in the quoted confidence intervals.

The total error budget for $H_0$ is dominated by non-SN systematics; the SN-specific uncertainty contributes less than a third, and control of photometric zero-point errors ensures Hubble constant determination is insensitive to cross-survey calibration at the 0.2 km/s/Mpc level, well below the “Hubble tension” scale (Brownsberger et al., 2021).

3. Systematic Uncertainties, Cross-Calibration, and Homogeneity

The rigorous tracking of systematic uncertainties is central to Pantheon+’s scientific credibility:

• Photometric Zero-points: Cross-survey offsets allowed to float within well-characterized priors; residual uncertainties primarily affect $\Omega_m$ and $w$, not $H_0$ (Brownsberger et al., 2021).
• Light-curve Model and Training: Full retraining of the SALT2 model on the Pantheon+ photometric/calibration system, systematic error propagation into covariances.
• Redshift and Peculiar Velocities: Multiple peculiar velocity reconstructions (e.g., 2MRS, 2M++) are incorporated; low-$z$ SNe allow explicit tracking of velocity-originated uncertainties.
• Selection and Bias Correction: BBC method models selection effects by constructing efficiency curves and applying bias corrections tuned through simulations.

Comparative analysis of duplicate SNe across surveys and paper of SNe sibling residuals in host galaxies constrain unmodeled survey- or host-dependent error contributions (Scolnic et al., 2021).

Systematic uncertainty in Hubble constant measurement is thus minimized, while for $\Omega_{m}$ and $w$ the uncertainty is sensitive to photometric cross-calibration, justifying the requirement for extensive homogeneous calibration.

4. Probes of Cosmic Isotropy and Anisotropy

Pantheon+ enables probing spatial isotropy at high precision, leveraging both full-sky coverage and careful treatment of sample inhomogeneity:

• Cosmic Isotropy Tests: Hemispherical mapping and local cosmographic expansion indicate spatial variation in $q_0$ and $H_0$ consistent with survey selection effects and sample inhomogeneity, with no statistically compelling evidence for large-scale deviation from isotropy in low-$z$ SN data (Andrade et al., 2018, Bengaly et al., 27 Feb 2024).
• Anisotropy Multipoles: Quadrupole and dipole multipoles in the Hubble and deceleration parameters, respectively, are detected at the $\sim2\sigma$ level in Pantheon+ using cosmographic and GR simulation-based modeling. For the Hubble parameter, the quadrupole amplitude is constrained to $<2.88\%$, with eigenvalues $\lambda_1 = 0.021\pm0.011$ and $\lambda_2\simeq 0$ at $z\simeq0.035$ (Cowell et al., 2022). The maximum induced shift in $H_0$ is $0.30$ km/s/Mpc, far smaller than the Hubble tension.
• Bulk Flow and Dipole Analyses: Advanced forward-modeling (jointly fitting for calibration, light-curve parameters, distances, and velocities) finds a significant ($\sim3\sigma$) dipolar zero-point in supernova brightness consistent with the direction and amplitude of local bulk flows and systematics expected from large-scale structure. When allowing for radially-dependent velocity fields, all signatures are consistent with the standard cosmological expectation—i.e., no unmodeled cosmic anisotropy is required (Stiskalek et al., 18 Sep 2025).

5. Impact on Cosmological Tensions and Compatibility with Other Probes

Pantheon+ plays a pivotal role in quantifying and understanding cosmological tensions, such as the difference between local Hubble constant measurements (e.g., SH0ES+Pantheon+) and Planck-inferred values from the CMB:

• Hubble Tension: Photometric and other SNe systematics cannot account for the $\sim 7$ km/s/Mpc Hubble tension; Pantheon+ SNe-only systematic errors on $H_0$ are subdominant ($<0.2$ km/s/Mpc) (Brownsberger et al., 2021, Brout et al., 2022).
• Tomographic and Statistical Cross-Checks: Tomographic binning finds no evidence for redshift evolution of $H_0$ or $\Omega_m$ at $>2\sigma$ in the Pantheon+ sample. The parameter space shifts in joint analyses are consistent with the tension persisting even after inclusion of external datasets (Wang, 2022).
• Statistical Dataset Concordance: Application of non-Gaussian Surprise statistics reveals model-dependent tensions, with $\sim2\sigma$ tension between Pantheon+&SH0ES and BAO+BBN in nonflat $w$CDM, and >3$\sigma$ in flat $\Lambda$CDM for the comparison of DESI BAO to Pantheon+ (Mello et al., 15 Aug 2024). Bayesian model selection, crossing statistics, and template deformation analyses indicate the Pantheon+ sample is internally consistent with flat $\Lambda$CDM, but that mild ($1–2\sigma$) discordances with other SNe compilations (e.g., DES5YR) remain (Matthewson et al., 4 Sep 2024).

6. Legacy and Role in Standard Candle Calibration

The Pantheon+ framework underpins efforts to refine Type Ia SNe as cosmological standard candles and to cross-calibrate alternative distance indicators:

• Absolute Magnitude Calibration: Model-independent (Gaussian process regression) calibration places $M_B=-19.395\pm0.015$ mag (using SNe+CC+BAO), validating the standardization of SNe Ia at percent-level accuracy (Dinda et al., 2022).
• Cross-Calibration of Alternative Probes: The Pantheon+ distance-redshift relation, reconstructed via GP regression, provides the cosmology-independent anchor for calibrating the evolving UV/X-ray luminosity relation in quasars, allowing quasar Hubble diagrams to remain consistent with SNe SEDs after accounting for redshift-dependent calibration coefficients (Li et al., 28 Aug 2024).
• Gravitational Lensing as a Probe: Multiple image pairs in the Pantheon+ sample are interpreted as strongly lensed SNe Ia by foreground compact objects (e.g., possible ultra-massive white dwarfs at $90$ and $702$ kpc), offering new local probes for mass, distance, and compact object demographics (Sanejouand, 7 Sep 2024).
• Model-Independent Expansion History: Spread-luminosity distance fitting (spread-LDF) analyses robustly reconstruct the acceleration history and supply evidence for a sign-changing generalized dark energy (GDE) pressure at $z>1$, challenging the assumption of a strictly constant $w$ (Çamlıbel et al., 9 Aug 2025).

7. Future Prospects and Theoretical Implications

Pantheon+ establishes the current standard for precision SNe cosmology, but identified limitations guide future efforts:

• Low-$z$ Systematics: The remaining dominant systematic uncertainty originates in modeling, calibrating, and homogenizing the low-redshift SNe subsample. Expansion with broader, well-monitored surveys and more SNe host galaxy measurements from facilities such as JWST will sharpen constraints on the Hubble constant, possible cosmic preferred axes, and dark energy evolution (Verma et al., 2023).
• Interpretation of Nontrivial Evolution: Evidence for time-varying absolute magnitude or sign-changing pressure in the effective dark energy sector, if substantiated by larger, higher-quality samples, may motivate extensions to simple $\Lambda$CDM, consideration of evolving gravitational strength, or alternative metrics for cosmic acceleration (Liu et al., 5 Jun 2024, Çamlıbel et al., 9 Aug 2025).
• Cosmological Principle and Homogeneity: Persistent but statistically marginal hints of isotropy violation (e.g., quadrupoles, cosmic preferred axes) require caution in interpretation, but future larger, more isotropic samples and next-generation large-scale structure surveys will further clarify the degree of cosmic homogeneity and isotropy.

In summary, the Pantheon+ Supernova Compilation represents a cumulative effort integrating extensive cross-survey photometry, calibration, and systematic control to deliver the most precise and robust SN-driven cosmological parameter constraints to date. The dataset is a critical resource for both current and next-generation cosmological analyses, standard candle calibration, and the empirical investigation of key cosmological principles.