Dark energy reconstruction analysis with artificial neural networks: Application on simulated Supernova Ia data from Rubin Observatory

TL;DR

This paper presents an analysis of Supernova Ia (SNIa) distance moduli $\mu(z)$ and dark energy using an Artificial Neural Network (ANN) reconstruction based on LSST simulated three-year SNIa data and demonstrates that the model-independent ANN reconstruction is consistent with both theoretical models.

Abstract

In this paper, we present an analysis of Supernova Ia (SNIa) distance moduli $μ(z)$ and dark energy using an Artificial Neural Network (ANN) reconstruction based on LSST simulated three-year SNIa data. The ANNs employed in this study utilize genetic algorithms for hyperparameter tuning and Monte Carlo Dropout for predictions. Our ANN reconstruction architecture is capable of modeling both the distance moduli and their associated statistical errors given redshift values. We compare the performance of the ANN-based reconstruction with two theoretical dark energy models: $Λ$CDM and Chevallier-Linder-Polarski (CPL). Bayesian analysis is conducted for these theoretical models using the LSST simulations and compared with observations from Pantheon and Pantheon+ SNIa real data. We demonstrate that our model-independent ANN reconstruction is consistent with both theoretical models. Performance metrics and statistical tests reveal that the ANN produces distance modulus estimates that align well with the LSST dataset and exhibit only minor discrepancies with $Λ$CDM and CPL.

Figures (5)

• Figure 1: ANN architecture founded by the hyperparameter tuning with genetic algorithms using nnogada.
• Figure 2: One and two-dimensional posterior distributions from Bayesian sampling for the free parameters of $\Lambda$CDM (left) and CPL (right) using SNIa data from Pantheon (1048 SNIa), Pantheon+ (1550 SNIa), and LSST simulations (5785 SNIa). For reference, dashed lines indicate the theoretical $\Lambda$CDM values of $w_0 = -1$ and $w_a = 0$.
• Figure 3: EoS for CPL with the three different datasets. We obtained these plots from the posterior distribution sampling using fgivenxhandleyfgivenx. It is interesting to note that for the LSST case, the $w=-1$ line (red dashed) marginally crosses the $1-\sigma$ range.
• Figure 4: Neural network reconstruction for distance modulus, $\mu(z)$ (black) with the standard deviation of the Monte Carlo Dropout predictions plus the modeled error (yellow region) using LSST data (green dots). Left: With $\Lambda$CDM and CPL using the values of the parameter estimation using LSST data. Right: In comparison with data points from other SNIa surveys, Pantheon and Pantheon+ using $\Lambda$CDM model only.
• Figure 5: Residual plot ($\delta\mu$) for two cosmological models as shown in figure legend. The residuals are computed between the LSST SNIa sim data (Fig. \ref{['fig:ann_reconstructions']}) and model-derived distance estimates. The right panel shows a Gaussian distribution of the corresponding residuals.