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 α, 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 α is non-zero. For small α there is an intermediate range where the potential is five-dimensional. Five-dimensional Newton constant decreases with increase of α 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.
Highlights
Newton potential for DGP brane-world scenario is examined when the extra dimension is semi-infinite
Randall-Sundrum(RS) scenario [5,6], one of the recent brane-world scenario developed by making use of the warped extra dimensions, provides an clue for the nature of 1/r-type Newton potential in our universe
Refs. [10,11] derived Newton potential arising due to the confined gravity on the brane when bulk space is a single copy of AdS5 from an aspect of the singular quantum mechanics(SQM). In this case the gravitational fluctuation equation is treated as an usual Schrodinger equation with a singular potential and it should be solved with incorporation of the self-adjoint extension technique [12]
Summary
Newton potential for DGP brane-world scenario is examined when the extra dimension is semi-infinite. For the case of the infinite extra dimension it is well-known that Newton potential is fivedimensional at long range and four-dimensional at short range [18]. For the case of the semi-infinite extra dimension the final form of Newton potential involves a self-adjoint extension parameter α, which makes an additional distance scale when α = 0. When α = 0, Newton potential is similar to that for the case of the infinite extra dimension.
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