On the Field Excursion Bound

TL;DR

This paper provides an alternative proof of a scalar field excursion bound in cosmology, showing it can only be saturated in non-accelerating universes and discussing its robustness against quantum and higher-derivative corrections.

Contribution

It offers a new proof of the field excursion bound, clarifies conditions for saturation, and discusses its implications in inflation and swampland contexts.

Findings

The bound can only be saturated in universes with zero acceleration.

Quantum corrections do not violate the bound in realistic inflation.

Higher-derivative corrections can violate the bound if superluminal sound speeds occur.

Abstract

In a recent work, Herderschee and Wall (HW) proved a bound on scalar field excursions in spatially flat FRW cosmologies. In this note, we give an alternate proof of their bound using the Friedmann equations, and we prove that it can be saturated only in universes with vanishing acceleration, $\ddot a =0$. We argue that in a realistic (eternal) inflation scenario, the bound is robust against quantum corrections and spacetime curvature, and it can be violated by higher-derivative corrections only at the expense of a superluminal speed of sound. We further speculate on possible connections between the swampland program and the vacuum estimates given in the work of HW.