Modified Newton's law, braneworlds, and the gravitational quantum well

Abstract

Most of the theories involving extra dimensions assume that only the gravitational interaction can propagate in them. In such approaches, called brane world models, the effective, 4-dimensional, Newton's law is modified at short as well as at large distances. Usually, the deformation of Newton's law at large distances is parametrized by a Yukawa potential, which arises mainly from theories with compactified extra dimensions. In many other models however, the extra dimensions are infinite. These approaches lead to a large distance power-law deformation of the gravitational newtonian potential $V_N(r)$, namely $V(r)=(1+k_b/r^b)V_N(r)$, which is less studied in the literature. We investigate here the dynamics of a particle in a gravitational quantum well with such a power-law deformation. The effects of the deformation on the energy spectrum are discussed. We also compare our modified spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultra cold neutrons moving above a mirror are studied. This comparison leads to upper bounds on $b$ and $k_b$.

11 pages, 1 figure

References in corpus (5)

• Minimal Length Uncertainty Relation and gravitational quantum well
• Remarks on the Noncommutative Gravitational Quantum Well
• Higher order corrections to the Newtonian potential in the Randall-Sundrum model
• Brane world corrections to Newton's law
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Cited by in corpus (7)

• Centrifugal quantum states of neutrons
• Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity
• On Newton's law in supersymmetric braneworld models
• GRASIAN: Towards the first demonstration of gravitational quantum states of atoms with a cryogenic hydrogen beam
• Cavity Optomechanical Probe of Gravity Between Massive Mechanical Oscillators
• Novel setup for detecting short-range anisotropic corrections to gravity
• Dynamical measurements of deviations from Newton's $1/r^2$ law