PantheonPlus & Union3 SNe Ia Cosmology

• PantheonPlus and Union3 are large compilations of spectroscopically confirmed Type Ia supernovae designed for precise cosmological parameter estimation.
• They employ advanced photometric calibration, light-curve modeling (SALT2/SALT3), and Bayesian frameworks (UNITY1.5) to rigorously control systematic uncertainties.
• Combined with complementary BAO and CMB data, these datasets refine measurements of the Hubble constant, dark energy parameters, and the late-time expansion history of the universe.

PantheonPlus and Union3 are contemporary, extensive compilations of spectroscopically confirmed Type Ia supernovae (SNe Ia) designed for precise cosmological inference, especially for measuring the Hubble constant ($H_0$), dark energy equation-of-state parameter ($w$), and reconstructing the late-time expansion history of the universe. These datasets differ in sample size, calibration methodology, light-curve fitting procedures, and statistical frameworks, leading to nuanced differences in derived cosmological parameters and systematic uncertainties. The interaction of these compilations with complementary datasets, particularly baryon acoustic oscillations (BAO), has allowed for rigorous cross-validation and testing of the $\Lambda$CDM paradigm and its extensions.

1. Dataset Composition and Survey Characteristics

PantheonPlus comprises 1,701 cosmology-grade SNe Ia drawn from 18 photometric surveys, with redshift coverage $z_{\rm min}\approx0.0008$ to $z_{\rm max}\approx2.26$ and a median $z\approx0.28$ (Scolnic et al., 2021). It applies stringent quality cuts to initial light-curve fits (1,778 converged SALT2 fits reduced by probability, coverage, stretch-color bounds, etc.) to achieve uniformity. Union3 extends this approach to an even larger sample: 2,087 SNe from 24 surveys, covering the identical redshift range $0.01 \leq z \leq 2.26$ (Rubin et al., 2023). Union3 integrates additional high-$z$ and nearby datasets, and releases homogeneous SALT3 light-curve fits.

Compilation	SNe Ia Count	Surveys Integrated	Redshift Range
Pantheon+	1,701	18	0.0008 -- 2.26
Union3	2,087	24	0.01 -- 2.26

The surveys aggregated involve multiple calibration systems, filters, and exposure strategies, necessitating elaborate inter-survey calibration (see Section 2).

2. Photometric Calibration and Light-Curve Modeling

PantheonPlus calibration proceeds via "Supercal+" [Brout et al.], which anchors all surveys to the Pan-STARRS1 (PS1) and CALSPEC standards with zeropoint ties of $\lesssim 7$ mmag; duplicate SNe confirm calibration precision at $\lesssim 5$ mmag for matches (Scolnic et al., 2021). All light curves are refit with the SALT2 model across 200–900 nm rest-frame. Systematic uncertainty sources include filter passbands, intrinsic scatter, host-mass corrections, and bias-correction terms derived from $2 \times 10^8$ SNANA simulations.

Union3 standardizes photometry via independent AB offset determination involving Landolt/CALSPEC, Smith/CALSPEC, PS1 aperture photometry, and passband shift modeling. SALT3—a retrained model encompassing the full rest-frame UV-optical domain—is utilized (Rubin et al., 2023). Calibration offsets and filter corrections are explicitly quantified, and the entire process is built into the UNITY1.5 Bayesian analysis framework (see Section 4).

Both compilations apply selection effects and crosschecks via duplicated SNe and stellar standards to ensure flux homogeneity.

3. Cosmological Distance Estimation and Systematics

The distance modulus for each SN is derived using Tripp-like estimators. In Pantheon+, the calibrated estimator is

$$\mu = m_B - M + \alpha x_1 - \beta c + \Delta_b(z) + \Delta_{\rm host}(z)$$

with $\alpha$ and $\beta$ fitted as nuisance parameters and $\Delta_b(z)$, $\Delta_{\rm host}(z)$ as selection and host-mass corrections. A covariance matrix $C_{ij}$ incorporates $\sim40$ sources of systematic uncertainty, including photometric zeropoints, SALT2 model errors, filter throughputs, MW extinction, and host-mass steps, added to a diagonal intrinsic scatter term ($\sigma_{\rm int}\approx0.105$ mag) (Scolnic et al., 2021).

Union3 employs the SALT3 standardization relation, marginalizing all latent parameters and systematics hierarchically (Rubin et al., 2023). Survey-specific unexplained dispersion and selection-depth modeling are explicit. Outlier modeling and per-survey systematics (zeropoints, passbands, extinction, peculiar velocities) are included as nuisance parameters in the joint posterior.

4. Statistical Frameworks: BBC vs. UNITY1.5

PantheonPlus uses BBC bias corrections and traditional likelihood maximization, focusing on selection function simulation and covariance propagation (Scolnic et al., 2021). Union3 introduces UNITY1.5—a full Bayesian hierarchical generative model—for simultaneous inference of population distributions, selection, latent SN parameters, outlier fraction, and cosmology (Rubin et al., 2023). All links between observed SN parameters and true cosmological distances are sampled, with mixing for outlier and unexplained dispersion components.

UNITY1.5 validation against simulated SN surveys demonstrates correct recovery of population, selection, and cosmological parameters, provided selection effects are explicitly modeled; omission results in catastrophic biases (e.g., $w_0 \gtrsim -0.95$).

5. Comparative Cosmological Inference and Consistency Checks

Both PantheonPlus and Union3 yield statistically consistent cosmological constraints when combined with BAO and CMB data. PantheonPlus finds, with Planck priors,

• $w = -1.000 \pm 0.030$
• $H_0 = 73.04 \pm 0.89$ km s$^{-1}$ Mpc$^{-1}$ (Scolnic et al., 2021)

Union3 + UNITY1.5 reports:

• $w = -0.957 \pm 0.035$
• $w_0 = -0.744 \pm 0.099$, $w_a = -0.79 \pm 0.37$; $\sim1.7$–$2.6\sigma$ evidence for “thawing” dark energy ($w_0>-1$, $w_a<0$) (Rubin et al., 2023).

Model-independent consistency analyses using crossing statistics and iterative smoothing show that any tensions between Pantheon+ and Union3 distance modulus curves are mild ($\sim2\sigma$ under strict flat $\Lambda$CDM fits), and entirely reconcilable to $\lesssim1\sigma$ within extended models allowing smooth Chebyshev polynomial deformations or higher-order corrections (Matthewson et al., 2024). No compelling evidence exists for cosmological inconsistency outside the assigned systematics.

6. Impact on Expansion History Reconstruction and BAO Calibration

Recent non-parametric reconstructions of late-time expansion history $E(z)$, combining DESI BAO with PantheonPlus or Union3, constrain $|E(z)/E_{\rm ref}(z)-1| \lesssim 10\%$ for $z \leq 2$. However, PantheonPlus data (with DESI BAO) robustly identifies localized features: a $z\sim0.5$ bump ($E(z)$ 5–8% above $\Lambda$CDM) and a $z\sim0.9$ depression (5–7% below), each significant at $>2\sigma$ (Jiang et al., 2024). When Union3 is employed instead, the bump’s amplitude drops to 4–6% ($\sim2\sigma$), and the depression is rendered insignificant.

Global calibration parameters, such as $\beta_{\rm BAO}=c/(r_d H_0)=29.90\pm0.33$, and derived sound horizon values, $r_d \approx 136.2$–$136.5$ Mpc (after imposing SH0ES $H_0$ prior), do not meaningfully depend on PantheonPlus/Union3 choice; the resulting “sound horizon tension” with Planck ($\Delta r_d \sim 11$ Mpc, $5\sigma$ significance) is nearly identical for both (Jiang et al., 2024).

7. Systematic Uncertainties, Limitations, and Future Directions

Both compilations have systematically quantified uncertainties at the few-mmagnitude level but differ in conservative versus minimal treatment (Union3 more conservative in propagation of small systematics) (Rubin et al., 2023). Areas of future improvement in both frameworks concern intergalactic dust modeling, host-mass evolution effects, and precise peculiar-velocity correction, as sample sizes and survey heterogeneity increase. UNITY1.5 and similar hierarchical Bayesian models will be essential as the number of cosmologically useful SNe increases by an order of magnitude, maintaining systematics below statistical thresholds.

This suggests that ongoing meticulous cross-survey calibration, light-curve retraining, and joint modeling with external probes (BAO, CMB, BBN) remain indispensable for robust cosmological inference from Type Ia supernovae in the era of large compilations. The persistence of the sound horizon tension and localized features in the expansion history motivate continued investigation into possible new physics in the early universe (Jiang et al., 2024).