Background-Independent Semiclassical Gravity from Relative Entropy at Finite Resolution: A Phenomenological Audit
Abstract
Building on the published finite-resolution, background-independent framework for local semiclassical gravity, this work audits its phenomenological consequences across cosmology and particle physics. The finite–continuum bridge and cosmoparticle consistency provide the organizing principles. Because the diffeomorphism-invariant Hilbert space does not factorize, the construction is formulated on a causal diamond with a boundary-completed algebra that supplies the edge data needed for a local Wheeler–DeWitt description. The operational state and semiclassical reference family then share this algebra, allowing their relative-entropy mismatch to define local dynamics as statistical inference within an entropic approach to quantum gravity. The topology-locked boundary capacity fixes an effective channel multiplicity N ≈ 1.23 × 10¹¹. Calibrating its coherent tensor fraction to Newton's constant gives a common matching scale Mₛ ≈ 3.02 × 10¹³ GeV. In the equilibrium KMS regime, the leading relative-entropy Hessian separates into tensor, vector, and scalar response blocks. A quasi-local heat-kernel expansion maps these responses to a matching-scale effective field theory, while completely positive trace-preserving updates describe the open-modular evolution between causal diamonds. The finite–continuum bridge separates the geometric spectral response from the internal matter trace. The internal algebra \( \mathcal A_F\simeq\mathbb C\oplus\mathbb H\oplus M_3(\mathbb C) \) organizes…
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