LADDER: Revisiting the Cosmic Distance Ladder with Deep Learning Approaches and Exploring its Applications

TL;DR

This work presents LADDER, a covariance-aware deep learning framework to reconstruct the cosmic distance ladder in a model-independent manner using Pantheon SNIa data. By treating $P(m|z)$ as a conditional normal $\mathcal{N}(\mu_\theta(z),\sigma_\theta(z))$ and leveraging a $K$-point conditioning scheme with KL-divergence losses, the method learns robust distance predictions and uncertainties that extrapolate beyond the training redshift range. An LSTM-based LADDER with $K=32$ achieves superior smoothness and monotonicity, outperforming other regressors and enabling applications such as model-independent Pantheon/Pantheon+ consistency checks, BAO pathology tests, and high-redshift GRB calibrations that yield competitive cosmological constraints. Additionally, LADDER can generate model-independent mock catalogs for future probes, offering a data-driven path to forecast cosmological outcomes without reliance on specific cosmological priors.

Abstract

We investigate the prospect of reconstructing the ''cosmic distance ladder'' of the Universe using a novel deep learning framework called LADDER - Learning Algorithm for Deep Distance Estimation and Reconstruction. LADDER is trained on the apparent magnitude data from the Pantheon Type Ia supernovae compilation, incorporating the full covariance information among data points, to produce predictions along with corresponding errors. After employing several validation tests with a number of deep learning models, we pick LADDER as the best performing one. We then demonstrate applications of our method in the cosmological context, including serving as a model-independent tool for consistency checks for other datasets like baryon acoustic oscillations, calibration of high-redshift datasets such as gamma ray bursts, and use as a model-independent mock catalog generator for future probes. Our analysis advocates for careful consideration of machine learning techniques applied to cosmological contexts.

Figures (6)

• Figure 1: Schematic overview of the training algorithm.
• Figure 2: Results of ablation studies and validation experiments with various models. (i-iii) Variation of error, smoothness and monotonicity with K respectively. MLP models do not produce smooth, monotonic results (except K=1), and the $K=1$ MLP is outperformed by the LSTM model at roughly the same smoothness and monotonicity. (iv) Prediction variation of models trained on $\Sigma|{\lambda}$ and $\Sigma_0$. When the covariance matrix is progressively corrupted with noise, the predictions change, thus demonstrating our approach's ability to model correlations.
• Figure 3: Testing Pantheon+ : Relative redshift distribution of the Pantheon and Pantheon+ datasets (left panel); Comparison between Pantheon-trained LADDER reconstruction vs Pantheon+ (right panel).
• Figure 4: Cosmological parameter constraints obtained from the Pantheon and Pantheon+ datasets vs LADDER predictions.
• Figure 5: Calibration of BAO -- Colored contours are LADDER predictions, dashed ones correspond to benchmark $\Lambda$CDM calibration.