From minimal-length quantum theory to modified gravity

TL;DR

This paper links generalized uncertainty principles with minimal length to extended gravity theories, deriving corrections to black hole entropy and light deflection, and constraining quantum gravity effects via astrophysical data.

Contribution

It develops a systematic method to connect GUP parameters with higher-order curvature terms in modified gravity theories, bridging quantum gravity phenomenology and classical gravity.

Findings

Derived modifications to Einstein's gravity from GUP-induced entropy corrections.

Established a mapping between GUP parameters and curvature coefficients.

Provided bounds on minimal length from light deflection measurements.

Abstract

In this work, we consider generalized uncertainty principles (GUPs) that incorporate a minimal length through generic momentum-dependent deformation functions. We thus develop a systematic approach connecting such a framework to effective gravitational actions extending general relativity. By examining quantum gravity-motivated corrections to black hole entropy induced by the GUP and employing Wald's formalism, we reconstruct modifications to Einstein's gravity within the contexts of $f(R)$ and $f(R, R_{\mu\nu} R^{\mu\nu})$ theories. In this way, we establish a direct mapping between the GUP parameters and the higher-order curvature coefficients in the gravitational Lagrangian. As an illustrative application, we compute corrections to the general relativistic prediction for light deflection, which in turn allows us to infer a stringent upper bound on the minimal measurable length. Our results show that GUP-induced effects can be consistently embedded into extended gravity theories, offering a promising framework for testing quantum gravity phenomenology through astrophysical and cosmological observations.