Newton Law in DGP Brane-World with Semi-Infinite Extra Dimension

TL;DR

This paper investigates how the Newtonian potential behaves in a DGP brane-world model with a semi-infinite extra dimension, revealing a transition from four-dimensional to seven-dimensional behavior depending on the scale and a parameter $eta$.

Contribution

It introduces a self-adjoint extension parameter in the DGP model with a semi-infinite extra dimension, showing its impact on the potential's dimensional behavior across scales.

Findings

Potential behaves as 7D at long range for nonzero $eta$

Intermediate range exhibits 5D behavior for small $eta$

Short range recovers 4D Newtonian potential

Abstract

Newton potential for DGP brane-world scenario is examined when the extra dimension is semi-infinite. The final form of the potential involves a self-adjoint extension parameter $\alpha$, which plays a role of an additional mass (or distance) scale. The striking feature of Newton potential in this setup is that the potential behaves as seven-dimensional in long range when $\alpha$ is nonzero. For small $\alpha$ there is an intermediate range where the potential is five-dimensional. Five-dimensional Newton constant decreases with increase of $\alpha$ from zero. In the short range the four-dimensional behavior is recovered. The physical implication of this result is discussed in the context of the accelerating behavior of universe.