Effective Lagrangians and Universality Classes of Nonlinear Bigravity

TL;DR

Damour and Kogan develop a fully nonlinear bigravity framework, introducing universality classes of two-metric effective Lagrangians and emphasizing ultra-local interactions between $g_L$ and $g_R$ via a potential $V(g_L,g_R)$. They show how such theories emerge naturally from brane worlds, certain Kaluza-Klein constructions, and noncommutative geometry, deriving concrete nonlinear actions and examining their linear limits. The work analyzes the dynamical structure (via EOM and ADM) and explores phenomenological implications, including a tensor-quintessence-like mechanism that could drive cosmic acceleration while preserving local GR tests. They argue that nonlinear bigravity may sidestep some classic massive-gravity pathologies but acknowledge critical open issues (ghosts, stability, and matching to local sources) that require further study (DKP1, DKP2).

Abstract

We discuss the fully non-linear formulation of multigravity. The concept of universality classes of effective Lagrangians describing bigravity, which is the simplest form of multigravity, is introduced. We show that non-linear multigravity theories can naturally arise in several different physical contexts: brane configurations, certain Kaluza-Klein reductions and some non-commutative geometry models. The formal and phenomenological aspects of multigravity (including the problems linked to the linearized theory of massive gravitons) are briefly discussed.

Figures (4)

• Figure 1: Regular spectrum on (Fig.1 a) versus bigravity (Fig.1 b) or quazi-localized gravity (Fig. 1 c). The last spectrum is continuous but the first band is very narrow in comparison with the gap between bands.
• Figure 2: Warped metric for single flat brane (Fig. 2a) and bounce for a two-brane configuration (Fig. 2b). $L_2$ is the separation between branes and $L_1$ is the position of the bounce. If $L_1 \ll L_2$ the metric is mostly concentrated on a right brane and if $L_2-L_1 \ll L_1$ then it is concentrated on the left brane.
• Figure 3: Manifold $\Gamma$ (Fig. 3a) is on the verge of splitting into two classically disconnected manifolds $\Gamma_1$ and $\Gamma_2$ (Fig. 3b). These two manifolds may be connected at the quantum level.
• Figure 4: Here $L_1$ is the position of the bounce. The left configuration is just the mirror image of the right one and the positions of the bounces are related by $\bar{L}_1 = L_2 -L_1$. Under this transformation left and right branes are exchange their roles and, at the same time, $\alpha_R =\exp(2L_1-L_2) \rightarrow \bar{\alpha}_R = \exp(2L_2 - L_1) = \alpha^{-1}_R$.