Pantheon+ Sample Overview

• Pantheon+ is a refined compilation of Type Ia supernovae featuring over 1700 light curves from approximately 1550 unique supernovae spanning a redshift range from 0.001 to 2.3.
• It employs an advanced covariance treatment at the individual supernova level and integrates SH0ES Cepheid-host calibration to enhance the precision of distance measurements and key parameters like H₀ and Ωₘ.
• The dataset underpins robust cosmological tests, enabling detailed studies of isotropy, systematic uncertainties, and extensions beyond ΛCDM in the late-time Universe.

Pantheon+ is the current “workhorse” Type Ia supernova sample for late-time cosmology, used to constrain the distance–redshift relation, the Hubble constant $H_0$, the matter density $\Omega_m$, and a wide range of isotropy, systematics, and beyond-$\Lambda$CDM questions (Bidenko et al., 2023). In the literature it is described both as a compilation of 1701 light curves from 1550 unique SNe Ia over $0.0011701 lightcurve measurements of 1534 SNe over $0.001Tang et al., 2023, Bidenko et al., 2023). A defining feature of Pantheon+ is its integration of the SH0ES distance ladder through Cepheid-host supernovae and its use of a full covariance treatment at the level of individual supernovae, which has made it a central dataset for precision studies of the late Universe (Perivolaropoulos et al., 2023, Bidenko et al., 2023).

1. Compilation, predecessor sample, and published descriptions

Pantheon+ is the direct successor to the original Pantheon sample, which combined 1048 SNe Ia over $0.01$z$ surveys, and HST high-$z$ samples (Scolnic et al., 2017). Pantheon+ expands this framework with more nearby supernovae, updated calibration, and a revised covariance treatment. One paper summarizes it as 1550 spectroscopically confirmed SNe Ia, 1701 light curves, 18 different surveys, and $z \in [0.00122,\,2.26137]$ (Wang, 2022). Another states that Pantheon+ is delivered as a table Pantheon+SH0ES.dat with 1701 rows and 47 columns plus a full $1701\times1701$ covariance matrix $\Omega_m$0 (Perivolaropoulos et al., 2023).

A concise way to read the literature is that Pantheon+ has a stable identity as the largest late-time SN Ia Hubble-diagram compilation in current use, but some analyses count light curves, some count unique supernovae, and some impose redshift cuts such as $\Omega_m$1, yielding different effective sample sizes (Bidenko et al., 2023, Tang et al., 2023).

Published description	Sample statement	Analysis context
Original Pantheon	1048 SNe Ia, $\Omega_m$2	Precursor compilation
Pantheon+	1701 light curves from 1550 unique SNe Ia, $\Omega_m$3	Isotropy analysis
Pantheon+	1701 lightcurve measurements of 1534 SNe, $\Omega_m$4	Covariance analysis

Pantheon+ also differs from Pantheon in how it handles systematics. Instead of estimating systematics in coarse bins, it constructs a covariance matrix at the level of individual SNe, a change repeatedly identified as one of the reasons the sample yields tighter and more robust constraints (Bidenko et al., 2023).

2. Standardization, calibration, and cosmological observables

Pantheon+ uses Type Ia supernovae as standardized candles. In the standard late-time analysis, the observed corrected peak magnitude $\Omega_m$5 is related to the distance modulus $\Omega_m$6 and an absolute magnitude $\Omega_m$7 through

$\Omega_m$8

with

$\Omega_m$9

For flat $\Lambda$0CDM,

$\Lambda$1

These relations are the basis for inferring $\Lambda$2 and $\Lambda$3 from the Pantheon+ distance–redshift relation (Bidenko et al., 2023).

In a light-curve and calibration language, Pantheon+ provides an observed distance modulus based on a modified Tripp relation. Before bias corrections,

$\Lambda$4

where $\Lambda$5 is the peak apparent $\Lambda$6-band magnitude, $\Lambda$7 is the stretch parameter, $\Lambda$8 is the color parameter, $\Lambda$9 is a selection-bias correction from simulations, and $0.001BEAMS with Bias Corrections (BBC) calibration, analyses often work with

$0.001

with the Tripp-like corrections folded into $0.001Tang et al., 2023).

A distinctive feature of Pantheon+ is its embedded calibration to SH0ES. One analysis notes that 77 supernovae are in galaxies that host Cepheids and are used to tie the SN absolute magnitude to the distance ladder (Tang et al., 2023). Another emphasizes that the table contains standardized SN apparent magnitude $0.001Perivolaropoulos et al., 2023). This is why Pantheon+ can function both as a Hubble-flow sample and as a calibrated rung in local-$0.001

3. Covariance architecture and the “missing covariance” question

Pantheon+ is unusual among SN compilations because its covariance structure is itself an object of direct scientific scrutiny. The published covariance matrix contains diagonal statistical terms and off-diagonal correlated systematics, and one targeted study asked whether there could still be additional redshift-correlated noise—“missing covariance”—large enough to bias $0.001Bidenko et al., 2023).

That study modeled any extra correlated component with a zero-mean Gaussian process added to the Pantheon+ covariance,

$0.001

using Matérn, RBF, and non-stationary kernels. The principal result was negative: there was no statistically significant evidence for missing covariance. For Pantheon+, the baseline fit gave

$0.001

while marginalizing over Matérn-GP covariance gave

$0.001

The shift in $0.001uncertainty increased only modestly (Bidenko et al., 2023).

The same analysis placed a $0.001confidence upper limit

$0.001

interpreted as about 20\% of the average statistical error per SN in Pantheon+. Bayes factors did not favor the GP-extended model over the baseline, with $0.001Bidenko et al., 2023). A plausible implication is that Pantheon+’s per-object covariance construction has already captured the dominant correlated uncertainties relevant for standard SN cosmology.

This robustness matters directly for the Hubble tension. The same work found that the strongest allowed extra covariance could reduce the Planck–Pantheon+ discrepancy from about $0.001 to about $0.01, but not remove it (Bidenko et al., 2023).

4. Cosmological constraints, tomography, and late-time model tests

Pantheon+ has been used both as a standalone SN probe and as part of larger multi-probe combinations. In a tomographic $0.01

$0.01

and

$0.01

With SH0ES calibration included, the same study obtained for the full sample

$0.01

Using equal redshift interval binning, it found that the first bin in the redshift range $0.01no obvious evidence of evolution of $0.01 (Wang, 2022).

The same tomographic study also showed how calibration changes the global interpretation of Pantheon+. When Pantheon+ was combined with cosmic microwave background, baryon acoustic oscillations, cosmic chronometers, galaxy clustering, and weak lensing data without calibration, it obtained

$0.01

With the Cepheid calibration included, the combined result shifted to

$z$0

which that analysis described as inconsistent with the Planck-2018 result at about $z$1 confidence level (Wang, 2022). This suggests that the decisive issue for late-time $z$2 inference is not an internal redshift evolution of Pantheon+ itself, but the absolute-calibration step.

Pantheon+ has also been used in beyond-$z$3CDM tests. One analysis found that Pantheon+ alone gives weak constraints on interacting dark energy and Hu–Sawicki $z$4 gravity, but in combination with CMB, BAO, and cosmic chronometers it yielded

$z$5

for the modified matter expansion rate in an interacting dark-energy model and

$z$6

at $z$7 in Hu–Sawicki $z$8 gravity. In a Gaussian-process reconstruction of the equation of state, the combination of Pantheon+, cosmic chronometers, and CMB indicated a quintessence-like dark-energy signal beyond the $z$9 confidence level in the redshift range $z$0 (Wang, 2022).

5. Isotropy, dipoles, and regional anisotropy claims

Pantheon+ has been a major testing ground for the cosmological principle. One dipole-modulated $z$1CDM analysis of the full sample reported that Pantheon+ is well consistent with a null dipole. For the full sample ($z$2, 1701 SNe in that analysis), it obtained

$z$3

with a poorly constrained direction, and concluded that the full Pantheon+ is consistent with a large-scale isotropic universe (Tang et al., 2023).

The same work, however, found a stable low-redshift feature. Restricting to $z$4, it reported

$z$5

toward

$z$6

which it described as appearing at about the $z$7 level. The direction is about $z$8 away from the CMB dipole, so the paper argued that the low-$z$9 anisotropy could not be purely explained by the peculiar motion of the local universe (Tang et al., 2023).

Other analyses using region-fitting or Padé-cosmography hemisphere comparisons reported stronger directional signals. A region-fitting analysis mapped all-sky $z \in [0.00122,\,2.26137]$0 and $z \in [0.00122,\,2.26137]$1 and found a local matter underdensity region toward

$z \in [0.00122,\,2.26137]$2

and a preferred direction of cosmic anisotropy

$z \in [0.00122,\,2.26137]$3

with statistical significances of 2.78$z \in [0.00122,\,2.26137]$4 and 2.34$z \in [0.00122,\,2.26137]$5 for the underdensity and 3.96$z \in [0.00122,\,2.26137]$6 and 3.15$z \in [0.00122,\,2.26137]$7 for the anisotropy under “Isotropy” and “Isotropy with real-data positions (RP)” tests, respectively (Hu et al., 2023). A Padé-based hemisphere comparison similarly found preferred directions for $z \in [0.00122,\,2.26137]$8 and $z \in [0.00122,\,2.26137]$9, with the $1701\times1701$0 anisotropy reported at 4.75$1701\times1701$1 and 4.39$1701\times1701$2 for the Isotropy and Isotropy with RP tests (Hu et al., 2024).

A later reanalysis revised the interpretation. Using both dipole fitting and hemisphere comparison, it found that the full Pantheon+ sample yields only a statistically weak dipole, while the low-$1701\times1701$3 subsample gives

$1701\times1701$4

at $1701\times1701$5 significance toward $1701\times1701$6. It further showed that this low-$1701\times1701$7 signal is predominantly driven by surveys 5, 56, 63, and 150, while the full-sample hemisphere anisotropy is primarily determined by the highly inhomogeneous SNLS subsample. Its conclusion was that the apparent anisotropy arises from local structures or the inhomogeneous distribution of the datasets rather than an intrinsic cosmic anisotropy (Zhou et al., 21 Jun 2026). Taken together, these studies indicate that Pantheon+ is highly informative for isotropy tests, but that low-$1701\times1701$8 structure and survey footprint remain inseparable parts of the interpretation.

6. Local-systematics debates, dust, and methodological extensions

Pantheon+ has also become a focal point for debates about local systematics in the SN distance ladder. One likelihood analysis replaced the single SN Ia absolute magnitude parameter $1701\times1701$9 with two magnitudes $\Omega_m$00 and $\Omega_m$01 separated by a transition distance $\Omega_m$02. For the full Pantheon+ sample it found

$\Omega_m$03

with

$\Omega_m$04

relative to the single-$\Omega_m$05 model. The paper interpreted much of this improvement as modeling the known volumetric redshift scatter bias at $\Omega_m$06, and noted that when all Hubble-diagram SNe with $\Omega_m$07 are removed the $\Omega_m$08 tension decreases from above $\Omega_m$09 to a little less than $\Omega_m$10 (Perivolaropoulos et al., 2023). This does not redefine Pantheon+ globally, but it identifies the very local regime as a special domain in which absolute-magnitude homogeneity is more delicate.

Dust and color systematics form a second specialized theme. Pantheon+ normally excludes very red supernovae from the cosmology sample, but one reanalysis reinstated 57 SNe Ia that were removed solely for high color, with colors up to $\Omega_m$11. Fitting separate color–luminosity relations for $\Omega_m$12 and $\Omega_m$13, it found the change in the color–luminosity coefficient to be consistent with zero. Simulations favored a model with a flat dependence of $\Omega_m$14 on colour over a declining dependence, and the authors concluded that the line-of-sight $\Omega_m$15 to SNe Ia is not a single value, but forms a distribution (Rose et al., 2022). This result speaks directly to how Pantheon+ should be interpreted as a standardized-candle dataset: the mean color correction remains usable, but the residual scatter is more naturally associated with an $\Omega_m$16 distribution than with a universal dust law.

Pantheon+ has also been repurposed as a methodological anchor outside SN-only cosmology. An ANN+BNN analysis used the Pantheon+ apparent magnitude–redshift relation and full covariance matrix to reconstruct $\Omega_m$17 without assuming a cosmological model, then used that reconstruction to calibrate low-$\Omega_m$18 gamma-ray bursts and extend a Hubble diagram to $\Omega_m$19. In that application, Pantheon+ served as the low-redshift, cosmology-independent calibration basis for GRB cosmology (Huang et al., 10 Jun 2025). A very different extension proposed that the Pantheon+ pair SN 2013aa–2017cbv may be two images of a single strongly lensed event, a possibility with negligible impact on global cosmological parameters given the size of the sample but of interest for data-set curation and strong-lensing phenomenology (Sanejouand, 2024).

Across these literatures, the stable picture is that Pantheon+ is an excellent dataset with unusually rich internal structure. It supports robust late-time $\Omega_m$20CDM inference, especially once calibration is specified; it shows no statistically significant missing covariance of the Gaussian-process type; it remains broadly consistent with large-scale isotropy; and its most persistent complexities cluster in the very low-$\Omega_m$21 regime, in survey geometry, and in dust- and calibration-related subproblems (Bidenko et al., 2023, Zhou et al., 21 Jun 2026).