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Strongly gravitationally lensed supernovae (glSNe) are emerging as a powerful, independent probe for measuring the expansion rate of the Universe, offering a unique pathway to address the persistent “Hubble Tension.” Our latest work, detailed in 2510.07637, leverages the recently discovered multiply-imaged Type Ia supernova (SN Ia) H0pe to rigorously test the gravitational lens models essential for this technique. This analysis, led by Aadya Agrawal, provides a critical assessment of the tools used for precision cosmology, highlighting both their potential and current challenges.

The Promise and Peril of Time-Delay Cosmography

The method of time-delay cosmography, first proposed by Sjur Refsdal in 1964 (10.1093/mnras/128.4.307), uses the time delays between the multiple images of a lensed transient to measure cosmological distances. Because light from the background source travels along different paths through the foreground lensing galaxy cluster, each path has a varying length and experiences a different gravitational potential. This results in observable time delays between the arrival of the SN light in each image. These delays are inversely proportional to the Hubble constant ($H_0$), providing a direct, one-step measurement that bypasses the traditional cosmic distance ladder.

However, the accuracy of this measurement hinges entirely on the fidelity of the lens model, which describes the mass distribution of the foreground cluster. Any systematic errors in the model’s prediction of the lensing potential, and thus the light travel times and image magnifications, will propagate directly into the inferred value of $H_0$. SN H0pe, the first glSN Ia with sufficiently long time delays to constrain $H_0$, provides an unprecedented opportunity to validate these models. The original analysis by Pascale et al. (10.3847/1538-4357/ad9928) utilized seven distinct, blindly constructed lens models to derive an $H_0$ value, highlighting the need to understand the variance and potential biases between different modeling approaches.

Using a Standard Candle to Measure the Models

Our study takes a novel approach: instead of using the lens models to measure cosmology, we use cosmology to test the lens models. The key is that SN H0pe is a Type Ia supernova, a “standardizable candle” whose intrinsic brightness is well-understood. This allows us to perform a purely observational test. The core methodology is as follows:

  1. De-magnify the Supernova: We take the observed photometry of SN H0pe’s three images and apply a correction to remove the gravitational magnification predicted by each of the seven lens models. If a model is accurate, this “de-magnified” light curve should represent the supernova as it would appear without any lensing.
  2. Fit for Distance: We then fit this intrinsic light curve using well-established SN Ia spectral energy distribution (SED) models, namely BayeSN (10.1093/mnras/stab3496) and SALT3-NIR (10.3847/1538-4357/ac93f9). This process yields a distance modulus ($\mu$), a measure of the supernova’s distance.
  3. Compare to Expectations: Finally, we compare this observationally-derived distance modulus to the value expected for a source at SN H0pe’s redshift ($z=1.783$) within a standard $\Lambda$CDM cosmology, as constrained by large SN Ia surveys like Pantheon+ (10.3847/1538-4357/ac8e04) and DES-5Y (10.3847/2041-8213/ad6f9f).

A Systematic Overestimation of Magnification

The results of our analysis reveal a clear and consistent trend: every one of the seven lens models, regardless of its underlying methodology (parametric, non-parametric, or hybrid), systematically overestimates the magnification of SN H0pe. This leads to inferred distance moduli that are significantly higher than expected, with a weighted mean offset of more than 1 magnitude ($\Delta \mu > 1$ mag).

This finding, while confirming a bias already suspected by the modeling teams, provides a robust, independent validation of the issue. It underscores a critical challenge for precision cosmology: if not accounted for, such magnification biases can introduce significant errors into cosmological parameter estimates, including $H_0$. Interestingly, our analysis shows that distance moduli derived from purely photometric and spectroscopic estimates of the magnification (which do not rely on a lens model) are in much better agreement with cosmological expectations.

This work highlights the invaluable role of lensed SNe Ia not just as cosmological probes, but as powerful diagnostic tools for refining our understanding of gravitational lensing itself. As next-generation surveys from facilities like the Vera C. Rubin Observatory, Nancy Grace Roman Space Telescope, and Euclid are poised to discover hundreds of such events, developing and validating robust lens models will be paramount. SN H0pe has shown us that these rare cosmic alignments are a crucial testbed for identifying and correcting the systematic uncertainties that must be overcome to realize the full potential of time-delay cosmography.

Matt Grayling

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