Natural modification of quantum uncertainty, modified gravity, and cosmology

TL;DR

This paper explores the connection between generalized uncertainty principles and modified gravity theories in cosmology, highlighting the importance of context when extending physical models and identifying Born-Infeld models as uniquely consistent across frameworks.

Contribution

It demonstrates the complex relationship between generalized uncertainty principles and modified gravity, emphasizing the need for careful consideration of model extensions in different physical contexts.

Findings

Most modifications lead to complications when connecting different frameworks.

Born-Infeld models are uniquely natural in both quantum uncertainty and gravity settings.

Abstract

A common approach in physics and mathematics is to extend and modify theories and frameworks by considering what is often described as a `natural' extension or modification by including higher-order terms or by introducing other non-linearities. We show that such an approach must be taken with care as physical models can be connected in indirect ways. What looks like a natural approach in one setting will likely not be natural in another. We use the flat Friedmann-Lemaitre-Robertson-Walker equations of cosmology to connect the generalized uncertainty principle to modified theories of gravity. A simple additional term in one setting leads to enormous complications in the other. We identify Born-Infeld models as the only ones which appear natural in both settings.