Fundamental nature of inflation’s geometric origin

Determine whether the early-universe inflationary phase is fundamentally driven by curvature (e.g., f(R)), torsion (e.g., f(T), Einstein–Cartan), non-metricity (e.g., f(Q)), scalar dynamics (e.g., non-minimally coupled scalars), or emergent geometry, by identifying decisive theoretical and observational criteria that can discriminate among these origins.

Background

The review synthesizes multiple geometric paradigms that can reproduce current data but arise from distinct underlying structures. Present observations often leave these mechanisms degenerate.

Resolving this foundational question will likely require a combination of theoretical advances (e.g., UV completion, stability) and high-precision measurements (e.g., tensor properties, non-Gaussianity, isocurvature).