Multibrane DGP model: Our universe as a stack of $(2+1)$-dim branes

TL;DR

This paper extends the DGP model to a multi-brane setup, showing how gravity and scalar fields behave differently at various scales, supporting the 'vanishing dimensions' concept where high-energy physics appears lower dimensional.

Contribution

The paper generalizes the DGP model to multiple parallel branes, analyzing scalar and gravitational propagation and revealing scale-dependent dimensional behavior.

Findings

At short distances, interactions follow (2+1)-dim laws.

At large distances, interactions follow (3+1)-dim laws.

Interactions perpendicular to branes become (3+1)-dim at low momenta.

Abstract

We consider scenario in which our $(3+1)$-dim universe is actually a dense stack of multiple parallel $(2+1)$-dim branes. For this purpose, we generalize the DGP model to a multi-brane case. We solve for the propagation of the scalar field and gravity in this setup. At short distances (high momenta) along the branes interactions follow the $(2+1)$-dim laws, while at large distances (low momenta) interactions follow the usual $(3+1)$-dim laws. This feature is inherited from the original DGP model. In the direction perpendicular to the brane, we show that interactions become $(3+1)$-dim at low momenta which are unable to resolve the interbrane separation. Thus, this is one of the explicit constructs of the "vanishing dimensions" scenario where high energy physics appears to be lower dimensional rather than higher dimensional.