Inflation with a stringy minimal length, reworked

TL;DR

This paper explores scalar field theories on de Sitter backgrounds incorporating the string-inspired generalized uncertainty principle (GUP), revealing a minimum length scale and analytical solutions, with implications for inflationary cosmology.

Contribution

It introduces a new representation of the GUP that allows exact solutions for scalar fields on de Sitter space and analyzes the resulting stringy cutoff effects on inflation.

Findings

Scalar fields cannot be quantized below the string scale H^{-1}

Derived analytical corrections to the two-point correlation function

Identified a stringy cutoff scale affecting inflationary models

Abstract

In this paper we revisit the formulation of scalar field theories on de Sitter backgrounds subject to the generalized uncertainty principle (GUP). The GUP arises in several contexts in string theory, but is most readily thought of as resulting from using strings as effective probes of geometry, which suggests an uncertainty relation incorporating the string scale $l_s$. After reviewing the string theoretic case for the GUP, which implies a minimum length scale $l_s$, we follow in the footsteps of Kempf and concern ourselves with how one might write down field theories which respect the GUP. We uncover a new representation of the GUP, which unlike previous studies, readily permits exact analytical solutions for the mode functions of a scalar field on de Sitter backgrounds. We find that scalar fields cannot be quantized on inflationary backgrounds with a Hubble radius $H^{-1}$ smaller than the string scale, implying a sensibly stringy (as opposed to Planckian) cutoff on the scale of inflation resulting from the GUP. We also compute $(H l_s)^2$ corrections to the two point correlation function analytically and comment on the future prospects of observing such corrections in the fortunate circumstance our universe is described by a very weakly coupled string theory.