2008/10/31 by Gonzalo A. Palma, Subodh P. Patil
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/04/005
published as JHEP 0904:005,2009 · To appear in JHEP. Sub-section discussing how our approach avoids certain ordering ambiguities added
arxiv created 2009/03/10 · openalex publication_date 2009/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ls. After reviewing the string theoretic case for the GUP, which implies a minimum length scale ls, 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 ls)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.