Softly Massive Gravity

TL;DR

This work develops a brane-induced gravity model in codimensions two and higher, where gravity on a 4D brane acquires a soft mass through a brane-localized Einstein-Hilbert term, yielding a crossover from 4D to higher-dimensional gravity. The authors show that 4D unitarity is preserved via a resonance-like graviton propagator with poles on nonphysical Riemann sheets, while 4D analyticity may be sacrificed (causality can be violated) at superhorizon scales, a feature that has been argued to assist with the cosmological constant problem. The tensor structure interpolates between 4D massless gravity at short distances and higher-dimensional gravity at large distances, with the details depending on the number of extra dimensions N and the parameter b; a spectral representation with a positive density holds in many regimes, indicating absence of a strong-coupling problem. The results provide a gravitational analogue of the Higgs mechanism via an infinite KK tower and highlight UV-regularization sensitivity, suggesting a viable alternative to 4D massive gravity for addressing cosmological-scale phenomena.

Abstract

Large-distance modification of gravity may be the mechanism for solving the cosmological constant problem. A simple model of the large-distance modification -- four-dimensional (4D) gravity with the hard mass term-- is problematic from the theoretical standpoint. Here we discuss a different model, the brane-induced gravity, that effectively introduces a soft graviton mass. We study the issues of unitarity, analyticity and causality in this model in more than five dimensions. We show that a consistent prescription for the poles of the Green's function can be specified so that 4D unitarity is preserved. However, in certain instances 4D analyticity cannot be maintained when theory becomes higher dimensional. As a result, one has to sacrifice 4D causality at distances of the order of the present-day Hubble scale. This is a welcome feature for solving the cosmological constant problem, as was recently argued in the literature. We also show that, unlike the 4D massive gravity, the model has no strong-coupling problem at intermediate scales.