Inflation without fine-tuning leaves a distinct fingerprint in perturbations

Working within a scalar-tensor theory where the kinetic term of a scalar field couples directly to the Einstein tensor, the authors derive the full perturbation equations for scalar, vector, and tensor modes across cosmic history. The coupling dominates early on, driving a quasi-de Sitter inflationary phase without a finely tuned potential, then fades to recover standard post-inflationary evolution. Analytical and numerical solutions show all three perturbation modes — including vector modes, which decay in ordinary inflation — are amplified during this inflationary stage. That amplification of vector modes is a clean observational discriminant from conventional slow-roll inflation.