From minimal-length quantum theory to modified gravity

2025/11/18 by D'Agostino, Rocco, Bosso, Pasquale, Luciano, Giuseppe Gaetano
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories

paper · doi:10.48550/arxiv.2511.14869

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_μν R^μν) 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.

Citations

• GUP Effective Metric Without GUP: Implications for the Sign of GUP Parameter and Quantum Bounce
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• String theory beyond the Planck scale
• Curvature squared terms and string theories
• A new type of isotropic cosmological models without singularity
• Renormalization of higher-derivative quantum gravity

Related

• Minimal Length in quantum gravity and gravitational measurements
• Effective field theory from Relativistic Generalized Uncertainty
• Generalized uncertainty principles, effective Newton constant and regular black holes
• The Modified Quantum Mechanics from the Covariant Generalized Uncertainty Principle
• Impact of generalized uncertainty principle on the accretion process within the asymptotically safe ambiance