Newton Law in Brane-World Scenario with 4d Induced Gravity: Singular Quantum Mechanical Approach

Abstract

From the viewpoint of the singular quantum mechanics the effect of the energy-dependent coupling constant for $\delta$-function potential is examined. The energy-dependence of the coupling constant naturally generates the time-derivative in the boundary condition of the Euclidean propagator. This is explicitly confirmed by making use of the simple 1d model. The result is applied to the linearized gravity fluctuation equation for the brane-world scenario with 4d induced gravity. Our approach generates $5d$ Newton potential at a certain intermediate range of distance between two test massive sources. For other range of distance 4d Newton potential is recovered.

11 pages, no figure, v2: Newton law is improved, will appear in PLB

References in corpus (7)

• The dS/CFT Correspondence
• Induced Gravity on RS Branes
• Newton potential in deSitter braneworld
• Correction terms to Newton law due to induced gravity in AdS background
• Compromise of Localized Graviton with a Small Cosmological Constant in Randall-Sundrum Scenario
• Logarithmic Correction to Newton Potential in Randall-Sundrum Scenario
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Cited by in corpus (6)

• Vacuum solutions of the gravitational field equations in the brane world model
• Weak gravity in DGP braneworld model
• Solar system tests of brane world models
• Newton Law on the Generalized Singular Brane with and without 4d Induced Gravity
• Inflaton perturbations in brane-world cosmology with induced gravity
• Newton Law in DGP Brane-World with Semi-Infinite Extra Dimension