Matter coupling in asymptotically Weyl-invariant gravity

Determine whether the algebraic matter constraints induced by minimally coupled matter in Palatini gravity persist in asymptotically Weyl-invariant gravity or are ameliorated by the curvature-dependent exponent \(n(R_*)\), and characterize the resulting effects on ultraviolet closure.

Background

The ultraviolet closure analysis applies only to pure gravity. In Palatini formulations, minimally coupled matter generally modifies the connection equation through the stress-energy trace and produces algebraic constraints that are absent in metric $f(R)$ theories. The unresolved question is whether the AWIG interpolation changes these constraints or their phenomenological and ultraviolet consequences.