Folded Inflation, Primordial Tensors, and the Running of the Scalar Spectral Index

TL;DR

The paper addresses whether a running scalar spectral index can be a natural outcome of inflation embedded in a high-dimensional landscape. It develops folded inflation, a multi-field framework where the inflaton follows a piecewise path with several corners, allowing a total field excursion $\sum_a |\Delta \phi_a|$ to exceed the Planck scale while individual fields remain sub-Planckian. It shows that tensor amplitudes remain governed by the overall energy density, while the scalar spectrum acquires running and potential features through corner-induced derivatives, with a relaxed bound $r \le \frac{1}{8}|n_h|$ unless the motion is effectively one-dimensional. The analysis predicts that sizable tensors ($r \gtrsim 0.08$) generally imply nontrivial running $d n_R/d\ln k$, and that even with smaller $r$ the spectrum can exhibit running or localized features due to corners, offering a qualitative link between the stringy landscape and observable CMB signatures. These results motivate further multi-field reconstructions and landscape-informed phenomenology to constrain inflationary trajectories in the early universe.

Abstract

I discuss folded inflation, an inflationary model embedded in a multi-dimensional scalar potential, such as the stringy landscape. During folded inflation, the field point evolves along a path that turns several corners in the potential. Folded inflation can lead to a relatively large tensor contribution to the Cosmic Microwave Background, while keeping all fields smaller than the Planck scale. I conjecture that if folded inflation generates a significant primordial tensor amplitude, this will generically be associated with non-trivial scale dependence in the spectrum of primordial scalar perturbations.