Probabilistic Inference of Cosmological Density Parameters from Synthetic Hubble Expansion Data of Varying SNR Using Diverse Artificial Neural Network Architectures

TL;DR

The paper tackles inferring the cosmological density parameters $Ω_{m,0}$ and $Ω_{Λ,0}$ from synthetic $H(z)$ data under a flat $Λ$CDM framework, addressing Hubble-tension-related questions while extending ParamANN with a broader set of neural architectures. It constructs a KDE-based noise model from 47 real low-$z$ $H(z)$ observations and generates 100,000 synthetic data realizations across three SNR regimes, training five ANN architectures (MLP, CNN, BiLSTM, CNN+BiLSTM, CNN+GRU) to recover the two parameters. Evaluation uses KS tests, 1-Wasserstein distance, and χ^2-based statistics (including GLS), with a balanced ranking to identify architecture performance across SNRs; results show BiLSTM excels at high/normal SNR, while CNN+GRU is strongest at low SNR, and all architectures align with ParamANN within 1σ but differ from Planck within >3σ, highlighting methodological differences. The work demonstrates that data-driven ANN inferences can rapidly estimate cosmological densities from $H(z)$ while emphasizing the need for broader priors, extended redshift ranges, and calibration diagnostics to improve compatibility with multi-probe Planck results.

Abstract

This paper builds upon ParamANN's novel approach (S. Pal & R. Saha 2024) of using ANNs to infer cosmological density parameters by determining optimal architecture for varying synthetic Hubble data SNRs in estimating the density parameters $Ω_{m, 0}$ and $Ω_{Λ, 0}$ across redshift values $z \in [0, 1]$. To generate the synthetic data, this study randomly sampled initial free parameter values at $z=0$ from theoretically motivated priors and evolved them backwards using the first Friedmann Equation to generate clean $H(z)$ curves. Then, this paper adds realistic noise of high, normal, and low SNR by sampling relative uncertainties from a Gaussian KDE on 47 real data observations compiled by A. Bouali et al. (2023). In the end, this study found that a RNN that uses BiLSTM is the most effective for high and normal SNR data across four quantitative metrics. On the other hand, a combination of convolution and recurrent layers that uses GRU performed the best for low SNR data across the same four metrics. A comparison between the results of this paper's ANN predictions and those of ParamANN shows that all architectures tested in this paper regardless of training SNR are statistically consistent within 1 standard deviation of ParamANN. However, most ANN results are not statistically consistent within 3 standard deviations of Planck Collaboration et al. (2020), showing a significant difference between ANN and the more traditional MCMC methods used by Planck collaboration.

Figures (3)

• Figure 1: Density histogram of the relative uncertainty of the real data compared to common distribution fits.
• Figure 2: Normalized Gaussian posteriors for each model. Solid lines: model posteriors at $k=0.5,1.0,2.0$ (from Table \ref{['tab:model-results']}). Dashed lines: Planck 2018 and ParamANN posteriors.
• Figure 3: (Continued) Same as Fig. \ref{['fig:posteriors']}, panels (g)–(j).