Are there really conformal frames? Uniqueness of affine inflation

TL;DR

This paper explores affine gravity's unique approach to scalar field inflation, emphasizing the invariance of inflationary parameters under field redefinition and the potential for rich cosmological phenomenology.

Contribution

It demonstrates the invariance of inflationary observables in affine gravity and extends the analysis to multifield scenarios, highlighting the emergent nature of the metric.

Findings

Inflationary parameters are invariant under field redefinition in affine gravity.

Affine gravity allows a transition from nonminimal to minimal couplings via field redefinition.

The approach suggests rich phenomenology in cosmology and astroparticle physics.

Abstract

Here we concisely review the nonminimal coupling dynamics of a single scalar field in the context of purely affine gravity and extend the study to multifield dynamics. The coupling is performed via an affine connection and its associated curvature without referring to any metric tensor. The latter arises a posteriori and it may gain an emergent character like the scale of gravity. What is remarkable in affine gravity is the transition from nonminimal to minimal couplings which is realized by only field redefinition of the scalar fields. Consequently, the inflationary models gain a unique description in this context where the observed parameters, like the scalar tilt and the tensor-to-scalar ratio, are invariant under field reparametrization. Overall, gravity in its affine approach is expected to reveal interesting and rich phenomenology in cosmology and astroparticle physics.