Constraints on Non-Newtonian Gravity from Recent Casimir Force Measurements

Corrections to Newton's gravitational law inspired by extra dimensional physics and by the exchange of light and massless elementary particles between the atoms of two macrobodies are considered. These corrections can be described by the potentials of Yukawa-type and by the power-type potentials with different powers. The strongest up to date constraints on the corrections to Newton's gravitational law are reviewed following from the E\"{o}tvos- and Cavendish-type experiments and from the measurements of the Casimir and van der Waals force. We show that the recent measurements of the Casimir force gave the possibility to strengthen the previously known constraints on the constants of hypothetical interactions up to several thousand times in a wide interaction range. Further strengthening is expected in near future that makes Casimir force measurements a prospective test for the predictions of fundamental physical theories.Comment: 20 pages, crckbked.cls is used, to be published in: Proceedings of the 18th Course of the School on Cosmology and Gravitation: The Gravitational Constant. Generalized Gravitational Theories and Experiments (30 April- 10 May 2003, Erice). Ed. by G. T. Gillies, V. N. Melnikov and V. de Sabbata, 20pp. (Kluwer, in print, 2003

Tests of the Gravitational Inverse-Square Law

We review recent experimental tests of the gravitational inverse-square law and the wide variety of theoretical considerations that suggest the law may break down in experimentally accessible regions.Comment: 81 pages, 10 figures, submitted by permission of the Annual Review of Nuclear and Particle Science. Final version of this material is scheduled to appear in the Annual Review of Nuclear and Particle Science Vol. 53, to be published in December 2003 by Annual Reviews, http://AnnualReviews.or

Jacobi elliptic solutions of lambda phi(4) theory in a finite domain

The general static solutions of the scalar field equation for the potential V(phi) = -1/2 M-2 phi(2) + lambda/4 phi(4) are determined for a finite domain in (1 + 1)-dimensional space-time. A family of real solutions is described in terms of Jacobi Elliptic Functions. We show that the vacuum-vacuum boundary conditions can be reached by elliptic cn-type solutions in a finite domain, such as that of the Kink, for which they are imposed at infinity. We prove uniqueness for elliptic sn-type solutions satisfying Dirichlet boundary conditions in a finite interval (box) as well the existence of a minimal mass corresponding to these solutions in a box. We defined expressions for the "topological charge," "total energy" (or classical mass) and "energy-density" for elliptic sn-type solutions in a finite domain. For large length of the box the conserved charge, classical mass and energy density of the Kink are recovered. Also, we have shown that using periodic boundary conditions the results are the same as in the case of Dirichlet boundary conditions. In the case of antiperiodic boundary conditions all elliptic sn-type solutions are allowed.15172645265

Casimir interaction between two magnetic metals in comparison with nonmagnetic test bodies

We present the complete results for the dynamic experiment on measuring the gradient of the Casimir force between magnetic (Ni-coated) surfaces of a plate and a sphere. Special attention is paid to the description of some details of the setup, its calibration, error analysis, and background effects. Computations are performed in the framework of the Lifshitz theory at nonzero temperature with an account of analytic corrections to the proximity force approximation and of surface roughness using both the Drude and the plasma model approaches. The theory of magnetic interaction between a sphere and a plate due to domain structure of their surfaces is developed for both out-of-plane and in-plane magnetizations in the absence and in the presence of spontaneous magnetization. It is shown that in all cases the magnetic contribution to the measured force gradients is much smaller than the total experimental error. The comparison between experiment and theory is done using the rigorous statistical method. It is shown that the theoretical approach taking into account dissipation of free electrons is excluded by the data at a 95% confidence level. The approach neglecting dissipation is confirmed by the data at more than 90% confidence level. We prove that the results of experiments with Ni-Ni, Ni-Au, and Au-Au surfaces taken together cannot be reconciled with the approach including free electrons dissipation by the introduction of any unaccounted background force, either attractive or repulsive. © 2013 American Physical Society

Thermal Casimir effect in Kerr spacetime with quintessence and massive gravitons

Starting from an analytical expression for the Helmholtz free energy we calculate the thermal corrections to the Casimir energy-density and entropy within nearby ideal parallel plates in the vacuum of a massless scalar field. Our framework is the Kerr spacetime in the presence of quintessence and massive gravitons. The high and low temperature regimes are especially analysed in order to distinguish the main contributions. For instance, in the high temperature regime, we show that the force between the plates is repulsive and grows with both the quintessence and the massive gravitons. Regarding the Casimir entropy, our results are in agreement with the Nernst heat theorem and therefore confirm the third law of thermodynamics in the present scenario.Comment: 15 pages, 4 figure