Scales of Gravity

TL;DR

The paper proposes a brane-world framework in which the quantum gravity scale $M_*$ can be extremely low ($\sim 10^{-3}$ eV) while the Standard Model UV cutoff $M_{ m SM}$ remains large. A brane-localized Einstein term induced by SM loops yields effective 4D gravity on the brane up to an enormous crossover scale $r_c = M_P^2/M_*^3$, effectively shielding the SM from strong bulk gravity. By modeling quantum gravity above $M_*$ with a string-like bulk spectrum, the authors show that the enormous multiplicity of bulk states does not destabilize low-energy physics due to derivative couplings and induced kinetic terms, keeping Newtonian gravity intact at observable scales. They derive a consistent lower bound on $M_*$ from sub-millimeter gravity tests, collider data, astrophysical cooling, and cosmology (all around $10^{-3}$ eV), and discuss distinctive phenomenology including black hole behavior and baryon-number-violating processes suppressed by $M_P$ rather than $M_*$. The framework yields testable predictions for both collider experiments and precision gravity tests, while preserving key SM features such as gauge coupling unification in supersymmetric extensions.

Abstract

We propose a framework in which the quantum gravity scale can be as low as $10^{-3}$ eV. The key assumption is that the Standard Model ultraviolet cutoff is much higher than the quantum gravity scale. This ensures that we observe conventional weak gravity. We construct an explicit brane-world model in which the brane-localized Standard Model is coupled to strong 5D gravity of infinite-volume flat extra space. Due to the high ultraviolet scale, the Standard Model fields generate a large graviton kinetic term on the brane. This kinetic term ``shields'' the Standard Model from the strong bulk gravity. As a result, an observer on the brane sees weak 4D gravity up to astronomically large distances beyond which gravity becomes five-dimensional. Modeling quantum gravity above its scale by the closed string spectrum we show that the shielding phenomenon protects the Standard Model from an apparent phenomenological catastrophe due to the exponentially large number of light string states. The collider experiments, astrophysics, cosmology and gravity measurements {\it independently} point to the same lower bound on the quantum gravity scale, $10^{-3}$ eV. For this value the model has experimental signatures both for colliders and for sub-millimeter gravity measurements. Black holes reveal certain interesting properties in this framework.