---
title: 'PantheonPlus: Cosmology with Type Ia Supernovae'
url: https://www.emergentmind.com/topics/pantheonplus
type: topic
---

# PantheonPlus: Cosmology with Type Ia Supernovae

Searching arXiv for PantheonPlus and closely related primary sources.
Pantheon+—commonly written PantheonPlus—is the state-of-the-art compilation and analysis of Type Ia supernovae for cosmology, extending the original Pantheon sample into a larger, cross-calibrated, and systematically propagated Hubble-diagram dataset. The original analysis contains 1701 light curves of 1550 distinct SNe Ia spanning \(z=0.001\) to \(2.26\), and combines a retrained SALT2 light-curve model, an unbinned covariance treatment, and direct integration with Cepheid-calibrated SH0ES hosts when an absolute distance ladder is required [2202.04077]. In subsequent usage, a distinction is usually made between **PantheonPlus** as a relative-distance supernova compilation and **PantheonPlusSH0ES** as the Cepheid-calibrated joint likelihood that directly constrains \(H_0\) [2312.01977].

## 1. Definition, scope, and data content

PantheonPlus is a heterogeneous but homogenized SN Ia compilation built from low-redshift samples, SDSS-II, SNLS, HST high-redshift samples, PS1, DES 3-year, Foundation, and related inputs, with the Pantheon+ analysis describing 1550 distinct SNe Ia represented by 1701 cosmologically usable light curves over \(0.001<z<2.26\) [2202.04077]. A key novelty of the release is the explicit inclusion of SNe in Cepheid-calibrated host galaxies, enabling a single likelihood that links local distance calibrators, nearby SNe, and Hubble-flow SNe within one covariance framework [2202.04077].

The compilation is used in two closely related but operationally distinct ways. In the first, PantheonPlus functions as a relative-distance Hubble diagram: the absolute magnitude is marginalized, and the dataset constrains the shape of \(H(z)\) and parameters such as \(\Omega_m\). In the second, often denoted PantheonPlusSH0ES, Cepheid host distances calibrate the SN absolute magnitude and convert the Hubble diagram into a direct late-time constraint on \(H_0\) [2312.01977]. Later cosmological analyses often apply a \(z>0.01\) cut to suppress peculiar-velocity contamination, leaving 1590 light curves in one implementation and 1580 likelihood data points in another [2510.23105], [2312.01977].

This distinction is not semantic. PantheonPlus alone is primarily a precision relative-distance probe, whereas PantheonPlusSH0ES is a full distance-ladder likelihood. Much of the apparent diversity in later cosmological inferences traces to which of these two objects is being used.

## 2. Cross-calibration, light-curve modeling, and systematic control

A central technical pillar of PantheonPlus is the SuperCal-Fragilistic recalibration program, which solves simultaneously for offsets in 25 photometric systems and 105 filters and yields a full calibration covariance matrix rather than survey-by-survey offset estimates [2112.03864]. This recalibration incorporates the updated HST CALSPEC flux scale, whose change relative to earlier implementations is on the order of \(1.5\%\) over \(\Delta\lambda \sim 4000\,\text{\AA}\) [2112.03864].

The recalibration is coupled to a retraining of the SALT2 light-curve model, producing the SALT2-B22 surface used in the Pantheon+ cosmology analysis [2202.04077]. The paper on the calibration pipeline shows that the change in calibration together with SALT2 retraining causes a net distance-modulus drift of \(d\mu/dz = 0.04\) mag over \(0<z<1\), establishing that recalibration and light-curve-model retraining cannot be treated as separable corrections [2112.03864].

PantheonPlus also adopts the BS21 dust-plus-intrinsic-scatter model with host-dependent color distributions and propagates calibration, selection, redshift, Milky Way extinction, peculiar-velocity, and training uncertainties into an unbinned covariance matrix [2202.04077]. The resulting calibration-only contribution to dark-energy constraints is quantified as \(\sigma_w=0.013\), roughly half the sample statistical uncertainty, while the SN calibration contribution to the SH0ES \(H_0\) error budget is below \(0.2~\mathrm{km\,s^{-1}\,Mpc^{-1}}\) [2112.03864]. This systematic program underlies the factor-of-two improvement in cosmological constraining power on \(w\) relative to the original Pantheon analysis [2202.04077].

## 3. Statistical construction of the Hubble diagram

PantheonPlus is built on SALT2 light-curve fitting, with the flux-amplitude parameter converted to a pseudo-\(B\)-band magnitude through
\[
m_B \equiv -2.5\log_{10}(x_0).
\]
Distances are then inferred with a modified Tripp relation,
\[
\mu = m_B + \alpha x_1 - \beta c - M - \delta_{\rm bias} + \delta_{\rm host},
\]
where \(\alpha\) and \(\beta\) describe stretch and color standardization, \(M\) is the fiducial SN absolute magnitude, \(\delta_{\rm bias}\) is the simulation-based bias correction, and \(\delta_{\rm host}\) is the host-mass correction [2202.04077]. In the baseline BS21 configuration, Pantheon+ reports \(\alpha = 0.148 \pm 0.004\) and \(\beta = 3.09 \pm 0.04\) [2202.04077].

Cosmological inference uses the usual luminosity-distance relation
\[
d_L(z)=(1+z)\,c\int_0^z\frac{dz'}{H(z')},
\]
and the model distance modulus
\[
\mu_{\rm model}(z)=5\log_{10}\!\left(\frac{d_L(z)}{10\,\mathrm{pc}}\right).
\]
The SN-only likelihood is a Gaussian in the residual vector,
\[
-2\ln\mathcal{L}=\chi^2=\Delta\vec{D}^{\,T}C_{\rm stat+syst}^{-1}\Delta\vec{D},
\]
with an unbinned \(1701\times1701\) covariance matrix that preserves survey-to-survey correlations and reduces the information loss associated with redshift binning [2202.04077]. Pantheon+ explicitly argues that binning inflates the systematic error on \(w\), with the appendix comparison showing a factor \(1.5\) increase relative to the unbinned treatment [2202.04077].

For PantheonPlusSH0ES, the residual vector is modified so that Cepheid-host SNe are compared to host-distance calibrators rather than to a cosmological model,
\[
\Delta D_i'=
\begin{cases}
\mu_i-\mu_i^{\rm Cepheid}, & i\in \text{Cepheid hosts},\\
\mu_i-\mu_{\rm model}(z_i), & \text{otherwise},
\end{cases}
\]
and the covariance includes both the SN and Cepheid blocks [2202.04077]. This is the formal step that turns PantheonPlus from a relative-distance compilation into a calibrated distance ladder.

## 4. Cosmological constraints in the original Pantheon+ analysis

The original Pantheon+ cosmology paper reports that SNe Ia alone give
\[
\Omega_M = 0.334 \pm 0.018
\]
in flat \(\Lambda\)CDM [2202.04077]. In flat \(w_0\)CDM, Pantheon+ alone gives
\[
w_0=-0.90\pm0.14,
\]
while Pantheon+ alone in flat \(w_0w_a\)CDM yields
\[
w_a=-0.1^{+0.9}_{-2.0},
\]
both consistent with a cosmological constant [2202.04077].

With Cepheid calibration included, PantheonPlusSH0ES gives
\[
H_0=73.5\pm1.1~\mathrm{km\,s^{-1}\,Mpc^{-1}}
\]
in flat \(w_0\)CDM and
\[
H_0=73.3\pm1.1~\mathrm{km\,s^{-1}\,Mpc^{-1}}
\]
in flat \(w_0w_a\)CDM [2202.04077]. The persistence of this calibrated \(H_0\) across background parameterizations is one reason PantheonPlusSH0ES became central to late-time distance-ladder analyses.

When combined with CMB and BAO, Pantheon+ substantially sharpens dark-energy constraints. The original paper quotes
\[
w_0=-0.978^{+0.024}_{-0.031}
\]
for flat \(w_0\)CDM and
\[
w_a=-0.65^{+0.28}_{-0.32}
\]
for flat \(w_0w_a\)CDM when Pantheon+ is combined with CMB and BAO [2202.04077]. In the same analysis, the non-accelerating point \((\Omega_M,\Omega_\Lambda)=(0,0)\) is excluded at \(4.4\sigma\) using SNe alone, and the paper concludes that systematic uncertainties in the SN distance ladder comprise less than one third of the total \(H_0\) uncertainty and cannot explain the Hubble tension [2202.04077].

## 5. PantheonPlus as a baseline in post-2022 cosmology

After 2022, PantheonPlus became a standard late-time baseline in a wide range of beyond-\(\Lambda\)CDM analyses. In full-shape early-dark-energy studies, the baseline combination
\[
\text{PlanckTTTEEE+lens}+\text{ext.\ BAO}+\text{PantheonPlus}
\]
already limits the EDE fraction to
\[
f_{\rm EDE}<0.0635 \quad (95\%)
\]
with
\[
h=0.6789^{+0.0062}_{-0.0095},
\]
whereas replacing PantheonPlus by the calibrated PantheonPlusSH0ES likelihood drives the preferred solution to
\[
H_0=71.73^{+0.82}_{-0.86}\ \text{or}\ 72.03^{+0.82}_{-0.87}~\mathrm{km\,s^{-1}\,Mpc^{-1}}
\]
with
\[
f_{\rm EDE}=0.1179^{+0.025}_{-0.022}\ \text{or}\ 0.1399^{+0.023}_{-0.022},
\]
depending on nuisance priors [2312.01977]. This illustrates how the difference between relative-distance PantheonPlus and calibrated PantheonPlusSH0ES propagates directly into EDE inference.

PantheonPlus is also routinely used as a conservative cross-check against DESY5. In a PEDE model with a free dark-matter equation of state, the combination CMB+DESI+PantheonPlus yields
\[
w_{\rm dm}=-0.00065\pm0.00032,
\]
whereas CMB+DESI+DESY5 gives
\[
w_{\rm dm}=-0.00093\pm0.00032,
\]
so the preference for \(w_{\rm dm}\neq0\) weakens from about \(3\sigma\) to about \(2\sigma\) when PantheonPlus is used [2506.09819]. A broader review of evolving dark energy reaches a similar conclusion: combinations that simultaneously include PantheonPlus and SDSS BAO significantly weaken the preference for CPL evolution, with CMB+PantheonPlus giving only \(0.1\sigma\) and CMB+DESI+PantheonPlus giving \(2.5\sigma\), lower than comparable DESY5 or Union3 combinations [2502.10264].

The same pattern appears in recent distance-based tests with FRBs, CC, BAO, and CMB. Using FRB+PantheonPlus+DESI+CC+CMB, one analysis reports
\[
w_0=-0.866\pm0.060,\qquad
w_a=-0.37^{+0.27}_{-0.25},
\]
but finds weaker Bayesian support for extended models than when DESY5 is substituted [2510.23105]. This suggests that PantheonPlus often functions as a comparatively conservative SN anchor in late-time model selection, even when its parameter constraints remain precise.

## 6. Model-independent applications and continuing significance

PantheonPlus has also become a standard input for model-independent reconstructions. A Gaussian-process reconstruction using PantheonPlus+SH0ES+GRB+OHD+DESI finds that the reconstructed dimensionless Hubble parameter \(E(z)\) is consistent with \(\Lambda\)CDM at the \(2\sigma\) level for \(z<2\), while the mean reconstructed dark-energy equation of state crosses \(w=-1\) at
\[
z_{\rm wt}=0.464^{+0.235}_{-0.120},
\]
a suggestive but not decisive deviation from a cosmological constant [2511.02220]. In a model-independent test of the cosmic distance duality relation, PantheonPlus+DESI DR2+CC gives, for the linear parametrization \(\eta(z)=1+\eta_0 z\),
\[
\eta_0=-0.004\pm0.017,
\]
supporting the CDDR within \(1\sigma\) and yielding results consistent with DES Dovekie [2603.27616]. In cosmography with strong-lensing time delays and DESI-DR2, the combination SGL+PantheonPlus+DESI-DR2 gives
\[
\Omega_{k0}=-0.036^{+0.045}_{-0.046},\quad
q_0=-0.477^{+0.054}_{-0.058},\quad
j_0=0.835^{+0.427}_{-0.394},
\]
consistent with flatness and with \(\Lambda\)CDM kinematics at current precision [2511.00788]. In a Buchert-backreaction setting fitted only to PantheonPlus+SH0ES, the inferred optical depth to reionization is
\[
\tau_{\rm reion}=0.0581^{+0.0105}_{-0.0096},
\]
with a modest reduction of the Hubble tension [2604.13718].

These later applications show that PantheonPlus is more than a large SN compilation. It is simultaneously a precision relative-distance dataset, a calibrated distance ladder when coupled to SH0ES, and a benchmark late-time geometric probe for model-independent and model-extended cosmology. A plausible implication is that much of its continuing importance lies in this dual role: PantheonPlus supplies stringent low-redshift distance information, while the choice between its uncalibrated and SH0ES-calibrated forms determines whether the analysis is testing late-time geometry alone or the full absolute cosmic distance scale.

Source: https://www.emergentmind.com/topics/pantheonplus