Latent-Space Gaussian Processes for Dark-Energy Reconstruction from Observational \(H(z)\) Data

TL;DR

This paper develops a Bayesian Gaussian-process framework to reconstruct dark-energy properties from observational Hubble data, comparing different latent space formulations and assessing their robustness and sensitivity.

Contribution

It introduces a latent-space Gaussian-process approach for dark-energy reconstruction, analyzing its performance and robustness against different priors and data qualities.

Findings

No strong preference between latent-f and latent-H reconstructions in real data.

Inferred dark-energy parameters are consistent with bcDM across priors.

High-redshift data improves detection of dark-energy evolution.

Abstract

Using the 37-point cosmic-chronometer subset of observational Hubble parameter (OHD) data, we develop a Bayesian Gaussian-process framework to reconstruct the normalized dark-energy density \(f(z)\) and equation of state \(w(z)\), focusing on how the choice of latent space affects the inference. We compare a Gaussian-process prior placed directly on \(f(z)\) with the conventional latent-\(H\) formulation, and also test a log-\(f\) branch that enforces \(f(z)>0\). We further analyze OHD-like mock data generated from fiducial \(\Lambda\)CDM and mildly evolving \(w_0w_a\) models, using both the observed redshift distribution and a higher-quality high-redshift setup. For real OHD, leave-one-out cross-validation shows no strong predictive preference between latent-\(f\) and latent-\(H\) reconstructions. The inferred \(f(z)\), \(w(z)\), and \(Om(z)\) remain consistent with \(\Lambda\)CDM across the tested external priors, while apparent \(Om(z)\) trends are prior sensitive and not robust evidence for dark-energy evolution. Residual differences between the two latent constructions are small, sign mixed, prior dependent, and mainly confined to the weakly constrained high-redshift tail. We therefore interpret the real-data results primarily as a methodological assessment. In mock tests, the framework responds to injected mild evolution in the reconstructed dark-energy quantities and \(Om(z)\), with detectability depending on method and data coverage. Improved high-redshift OHD reduces the discrepancy between latent constructions and makes the \(Om(z)\) response more consistently detectable. The latent-\(f\) approach is therefore a viable alternative to latent-\(H\), while current constraints are limited mainly by sparse high-redshift OHD and dependence on external priors.