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 $k_b$.

arXiv comment11 pages, 1 figure

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• Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity
• On the use of the proximity force approximation for deriving limits to short-range gravitational-like interactions from sphere-plane Casimir force experiments
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• On Newton's law in supersymmetric braneworld models
• GRASIAN: Towards the first demonstration of gravitational quantum states of atoms with a cryogenic hydrogen beam
• Planck-Scale Corrections to Friedmann Equation
• Unparticle inspired corrections to the Gravitational Quantum Well
• Probing Short Gravity using Temporal Lensing
• Cavity Optomechanical Probe of Gravity Between Massive Mechanical Oscillators
• Proposed experimental test of Randall-Sundrum Models
• Short Distance Modification of a Gravitational System and its Optical Analog
• Novel setup for detecting short-range anisotropic corrections to gravity
• Dynamical measurements of deviations from Newton's $1/r^2$ law