# A Note on String Excitations and the Higuchi Bound

## TL;DR

This paper examines the interaction of high spin string excitations with the Higuchi bound in de Sitter space, revealing that string theory remains consistent if the string scale exceeds the Hubble scale, but requires modifications at high energies.

## Contribution

It identifies the point along the Regge trajectory where the Higuchi bound is violated and discusses the implications for string scale and trajectory modifications in de Sitter space.

## Key findings

- Higuchi bound violation occurs at a string length of order the Hubble scale.
- String theory remains consistent if the string scale exceeds the Hubble scale.
- A bound on the string scale is derived: M_s > sqrt(H M_p).

## Abstract

In this brief note we consider the interaction between high spin excitations in string theory along the Regge trajectory and the Higuchi bound in de Sitter space. There is always a point along the Regge trajectory where the Higuchi bound is violated. However, this point precisely coincides with a string whose length is of order the de Sitter Hubble scale. String theory therefore manifests no immediate inconsistency as long as the string scale $M_s$ is above the Hubble scale $H$. However, an implication is that the Regge trajectory must be significantly modified at some ultraviolet scale. Insisting that this modification should occur no earlier than the Planck scale would lead to a bound on the string scale of $M_s > \sqrt{H M_p}$.