Maximal momentum GUP leads to quadratic gravity

Quantum theories of gravity predict interesting phenomenological features such as a minimum measurable length and maximum momentum. We use the Generalized Uncertainty Principle (GUP), which is an extension of the standard Heisenberg Uncertainty Principle motivated by Quantum Gravity, to model the above features. In particular, we use a GUP with modelling maximum momentum to establish a correspondence between the GUP-modified dynamics of a massless spin-2 field and quadratic (referred to as Stelle) gravity. In other words, Stelle gravity can be regarded as the classical manifestation of a maximum momentum and the related GUP. We explore the applications of Stelle gravity to cosmology and specifically show that Stelle gravity applied to a homogeneous and isotropic background leads to inflation with an exit. Using the above, we obtain strong bounds on the GUP parameter from CMB observations. Unlike previous works, which fixed only upper bounds for GUP parameters, we obtain both lower and upper bounds on the GUP parameter. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This study utilizes the Generalized Uncertainty Principle to model features of quantum gravity and explores the applications of Stelle gravity in cosmology. It shows that Stelle gravity can be considered as a classical manifestation of maximum momentum and the GUP. Strong constraints on the GUP parameter are obtained from CMB observations, providing both lower and upper bounds.