See-Saw Modification of Gravity

TL;DR

The paper proposes a brane-world scenario with two or more infinite-volume extra dimensions in which gravity on the brane remains effectively 4D at observable distances but crosses over to higher-dimensional behavior at large scales. By incorporating an induced 4D Einstein-Hilbert term and higher-derivative regularization, the authors derive the Green's functions that govern inter-brane gravity and identify a robust link between ultraviolet and infrared gravity modification scales. Crucially, they argue that the crossover distance and the fundamental gravity scale are rigidly correlated, yielding a fixed $M_* \sim 10^{-3}$ eV and predicting observable modifications at both $\sim 0.1$ mm and the Hubble scale $H_0^{-1}$. The results are testable with table-top gravity experiments and cosmological observations, and hold for both thin and thick branes, providing a concrete avenue to address infrared modifications of gravity and related cosmological issues.

Abstract

We discuss a model in which the fundamental scale of gravity is restricted to 10^{-3} eV. An observable modification of gravity occurs simultaneously at the Hubble distance and at around 0.1 mm. These predictions can be tested both by the table-top experiments and by cosmological measurements. The model is formulated as a brane-world theory embedded in a space with two or more infinite-volume extra dimensions. Gravity on the brane reproduces the four-dimensional laws at observable distances but turns to the high-dimensional behavior at larger scales. To determine the crossover distance we smooth out the singularities in the Green's functions by taking into account softening of the graviton propagator due to the high-dimensional operators that are suppressed by the fundamental scale. We find that irrespective of the precise nature of microscopic gravity the ultraviolet and infrared scales of gravity-modification are rigidly correlated. This fixes the fundamental scale of gravity at 10^{-3} eV. The result persists for nonzero thickness branes.