Universal Nonminimal Coupling-to-Starobinsky Matching and a Single-Field Attractor

TL;DR

This paper proves a universal correspondence between nonminimal couplings and Starobinsky inflation, providing a frame-independent scalaron effective theory and precise CMB predictions.

Contribution

It establishes a frame-independent scalaron EFT in quadratic gravity and clarifies the algebraic structure of Palatini $f(R)$ models, enabling universal matching to $R^2$ inflation.

Findings

Universal matching from nonminimal couplings to $R^2$ sector.

Frame-independent scalaron effective field theory.

Quantitative single-field attractor bound with CMB predictions.

Abstract

We establish an off-shell commutativity theorem in 4D parity-even quadratic gravity that the Hubbard-Stratonovich/Legendre lifts, algebraic elimination of auxiliaries, including the torsionless Palatini connection, and Jordan-Einstein Weyl rescalings commute at the action level up to boundary terms. This yields a frame-independent characterization of the propagating degrees of freedom and isolates a universal scalaron EFT in the metric branch, while clarifying the algebraic nature of the Palatini $f(R)$ scalar. We obtain, as a result, a frame-universal matching from the generic nonminimal couplings to a positive $R^2$ sector and a quantitative single-field attractor bound, enhanced by a $1/\Delta N$ selection term, providing sharp and falsifiable CMB targets.