Multi-Brane Worlds and modification of gravity at large scales

TL;DR

The paper analyzes gravity modification in multi-brane worlds with mixed tensions, showing anomalously light KK states arise when a negative-tension brane sits between positive-tension branes. It develops and contrasts three configurations—the three-brane ++- model, the four-brane +--+ multigravity model, and a crystalline AdS5 lattice—demonstrating how the KK spectrum and brane couplings yield gravity that transitions from 4D to 5D and back to 4D across different distance scales. By deriving mass spectra, couplings, and spectral densities, it uncovers regimes of bigravity and GRS-like behavior, and clarifies how multigravity can emerge from brane tunneling and band-structure effects. The discussion addresses ghost radion instabilities and proposes decoupling mechanisms via radion dynamics or higher-dimensional tensor structure, highlighting both the phenomenological potential and the stability challenges of such brane-world scenarios.

Abstract

We discuss the implications of multi-brane constructions involving combinations of positive and negative tension brane and show how anomalously light KK states emerge when negative tension ''-'' branes are sandwiched between ''+'' branes. We present a detailed study of a ''+--+'' brane assignment which interpolates between two models that have been previously proposed in which gravity is modified at large scales due to the anomalously light states. We show that it has the peculiar characteristic that gravity changes from four dimensional (4D) to 5D at large distances and returns to 4D at even larger scales. We also consider a crystalline universe which leads to a similar structure for gravity. The problems associated with intermediate negative tension branes are discussed and a possible resolution suggested.

Figures (6)

• Figure 1: The brane locations in the three-brane $^{\prime \prime }++-^{\prime \prime }$ model. The bulk curvature between the $^{\prime \prime }+^{\prime \prime }$ branes is $k_{1}$ and between the $^{\prime \prime }+^{\prime \prime }$ and $^{\prime \prime }-^{\prime \prime }$ brane is $k_{2}$.
• Figure 2: $^{\prime\prime}+--+^{\prime\prime}$ configuration with scale equivalent $^{\prime\prime}+^{\prime\prime}$ branes. The distance between the $^{\prime\prime}+^{\prime\prime}$ and $^{\prime\prime}-1/2^{\prime\prime}$ branes is $l=L_1=L_3-L_2$ while the distance between the $^{\prime\prime}-1/2^{\prime\prime}$ branes is $l_-=L_2-L_1$. The curvature of the bulk between the $^{\prime\prime}+^{\prime\prime}$ and $^{\prime\prime}-1/2^{\prime\prime}$ branes is $k$.
• Figure 3: The behaviour of the mass of the first five KK states in the three regions of simple $x$, $x_{-}$ dependence. The first dot at zero stands for the graviton.
• Figure 4: The behaviour of the coupling, $a(m),$ in the limit of $x_{-}\gg e^{2x}$. Three regions of interest are indicated. The region $m>m_{0}$ gives rise to short distance corrections. The $m_{1}\ll m\ll m_{c}$ region gives rise to 4D gravity at intermediate distances and 5D gravity at ultra large distances. For distances $r\gg m_{1}^{-1}$, the zero mode gives the dominant contribution and thus we return to 4D gravity.
• Figure 5: The Crystal Universe made up of an infinite array of $^{\prime \prime }+^{\prime \prime }$ and $^{\prime \prime }-^{\prime \prime }$ branes with lattice spacing $l$ and bulk curvature $k$.