Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-01-18
Class.Quant.Grav.24:855-866,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
11 pages, 1 figure
Scientific paper
10.1088/0264-9381/24/4/006
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 $k_b$.
Buisseret Fabien
Mathieu Vincent
Silvestre-Brac Bernard
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