Study Classifies Linear Ricci-Trace Deformations in Modified Gravity Theories
A new preprint on arXiv analyzes a class of modified gravity theories known as Rastall-type models, showing that two commonly used mathematical parametrizations are algebraically equivalent only under specific simultaneous transformations of both the deformation parameter and the gravitational coupling constant. The work is structural rather than observational, aiming to resolve ambiguities in how parameters are defined and compared across the literature. The findings matter because conflicting equivalence claims in the Rastall gravity literature have created confusion about whether different formulations represent genuinely distinct physics or mere notational differences.
Researchers have submitted a 23-page preprint to arXiv examining linear Ricci-trace deformations of Einstein's general relativistic field equations, a framework associated with so-called Rastall gravity. The paper demonstrates that two parametrizations frequently appearing in the literature are algebraically isomorphic, but only if both the deformation parameter and the bare gravitational coupling are transformed simultaneously — a condition not always recognized in prior work. Crucially, the authors distinguish algebraic equivalence from operational equivalence: once a fixed laboratory stress tensor and a measured Newton constant are specified, the parameter map reduces to a passive reparametrization only at the standard Einstein point, meaning the two formulations can yield physically distinct predictions away from that limit. The study also derives the corresponding cosmological (FLRW) perfect-fluid equations for Rastall-type models and examines degenerate cases such as vacuum, radiation, dust, and the traceless singular point. Additionally, the paper carefully separates Rastall-type Ricci-trace deformations from Unimodular Gravity, noting that while both involve the trace sector of the field equations, they differ fundamentally in origin: Unimodular Gravity arises from a restricted variational principle and treats the cosmological constant as an integration constant rather than an algebraic modification. The result is intended as a compact operational classification to help standardize how Rastall-type models are compared and tested.
What's missing
The paper has not yet undergone peer review. Open questions include whether any parametrization within this class produces observationally distinguishable predictions from standard GR.
What different sources said
- arXiv astro-phCenter
Linear Ricci-Trace Deformations and Operational Equivalence in Rastall-Type Gravity
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