Physics-Informed Neural Networks Reconstruct Redshift-Dependent Barrow Exponent in Holographic Dark Energy

The study embeds the generalized Barrow holographic dark energy continuity equation directly into the neural network loss function, allowing Δ(z) to be inferred non-parametrically rather than assumed constant or given a preset functional form. Training on 1701 supernovae, 13 DESI DR2 BAO points, and 32 cosmic chronometers produces a smooth, negative-tilted reconstruction whose 1σ band still includes both Δ=0 and mildly negative constants. This approach bypasses the usual parametric priors that have historically masked possible scale dependence in horizon entropy.

Barrow holographic models link cosmic acceleration to quantum-gravitational corrections of the Bekenstein-Hawking entropy via the exponent Δ. Earlier analytic treatments assumed Δ fixed, limiting their ability to test whether deformations grow or decay across cosmic epochs. The PINN reconstruction shows that any such evolution remains statistically mild at present, yet the direction toward negative Δ aligns with recent indications that holographic dark energy may require entropy suppression rather than enhancement to match late-time data.

The result connects to broader efforts using machine learning for equation-of-state reconstruction, such as those applied to w(z) with similar datasets. It also highlights a methodological shift: instead of post-processing derived quantities, the entropy parameter itself becomes an output of the constrained network. Future surveys with tighter BAO and supernova systematics will decide whether the mild negative trend crosses significance thresholds or reverts to constancy.

Key limitation remains the modest number of chronometer points and the single assumed interaction form between dark energy and the Barrow-modified horizon; larger, homogeneous datasets from Euclid and Roman will be required to break these degeneracies.