Neural Network Reconstruction Finds Kaniadakis Holographic Dark Energy No Better Than LambdaCDM on Pantheon+SH0ES Data

The study trained bootstrap deep ensembles on mock catalogs generated from fiducial KHDE parameters (c=1.15, beta=0.30, Omega_m=0.30) to map redshift to distance modulus with analytic derivatives for H(z) and w(z). Pantheon+SH0ES mocks achieved 3.2% H(z) precision versus 6.0% for Pantheon alone, and Cepheid calibration proved essential to avoid H0 bias of 7 km/s/Mpc. On 1657 real supernovae with full covariance the model reproduced LambdaCDM benchmarks yet left beta unconstrained because its imprint on mu(z) is only 0.009 mag.

This approach illustrates how neural networks can perform model-independent reconstructions of exotic dark energy while remaining anchored to observable data. Related work on holographic dark energy (e.g., 2023 JCAP analyses of Tsallis and Kaniadakis variants) similarly finds parameter degeneracies that only future surveys can break. The preprint correctly flags that direct MCMC fits recover injected values, confirming the network pipeline does not introduce bias beyond the data's intrinsic signal strength.

The key limitation is the weak observational signature of the beta parameter, which current supernova precision cannot resolve at high significance. Larger samples from LSST or Roman Space Telescope, combined with BAO and CMB cross-correlations, would be required to test whether KHDE offers any improvement. The analysis correctly avoids claiming new physics from an unconstrained parameter.