Maximal momentum GUP leads to quadratic gravity

TL;DR

This paper links a maximum momentum GUP to quadratic gravity, showing that Stelle gravity emerges from GUP-modified dynamics and can explain cosmological inflation, providing bounds on GUP parameters from CMB data.

Contribution

It establishes a novel connection between GUP with maximum momentum and quadratic gravity, interpreting Stelle gravity as a classical manifestation of GUP effects.

Findings

Stelle gravity can be derived from GUP with maximum momentum.

Application of Stelle gravity to cosmology predicts inflation with exit.

Strong bounds on GUP parameters are obtained from CMB observations.

Abstract

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 \emph{lower and upper bounds} on the GUP parameter.