What does this research mean for the field?

ψ-Gravity provides a covariant gravitational framework that explains late-time curvature evolution and reproduces key cosmological observations, including the fixed growth index γ ≈ 0.64 and the suppression of the S₈ tension. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

The aim is to establish a new gravitational theory that incorporates a retentive divergence constraint and investigates its implications on curvature evolution.

March 2, 2026Open Access

ψ-Gravity: A Covariant Retentive Theory of Curvature with a Structural Divergence Constraint

Puntos clave

The aim is to establish a new gravitational theory that incorporates a retentive divergence constraint and investigates its implications on curvature evolution.
Developed the ψ-Gravity framework with a Retentive Divergence Constraint (RDC).
Conducted a stability analysis to ensure theory consistency.
Provided the full Lagrangian and covariant derivation of the RDC.
Explored predictions relevant to Euclid DR1 and Rubin LSST.
Reproduced the observed fixed growth index γ ≈ 0.64.
Identified a structural transition at z† ≈ 1.7.
Demonstrated suppression of the S₈ tension.
Observed Mirror Residuals in weak-lensing maps.
Ensured the theory remains ghost-free and consistent with General Relativity.

Resumen

This work presents ψ-Gravity, a covariant gravitational framework in which late-time curvature evolution is governed by a Retentive Divergence Constraint (RDC). The theory preserves full diffeomorphism invariance through effective curvature conservation, while allowing the bare Einstein tensor to acquire a structural correction sourced by the retentive field Δψ and nodes Ξ. ψ-Gravity reproduces the observed fixed growth index γ ≈ 0.64, the structural transition at z† ≈ 1.7, the suppression of the S₈ tension, and the appearance of Mirror Residuals in weak-lensing maps. It remains ghost-free, GR-consistent in early- and high-density limits, and lies outside all known Horndeski/DHOST classes. This article provides the full Lagrangian, covariant derivation of RDC, stability analysis, and falsifiable predictions relevant for Euclid DR1 and Rubin LSST.

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