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