Search Results (6)

This entry surveys the role of extra dimensions in Newtonian quantum cosmology, with particular emphasis on large, compactified, and warped dimensional geometries and their impact on the Newtonian potential in the early universe. The discussion begins with a review of Kaluza–Klein type toy models, followed by models with large extra dimensions in which gravity propagates into a higher-dimensional bulk, producing Yukawa-like modifications to the inverse-square law at submillimeter scales. Compactification schemes on toroidal and spherical dimensions are then examined, yielding the spectrum of Kaluza–Klein modes and quantifying their corrections to the Newtonian potential. Warped extra dimensions of the Randall–Sundrum type are also considered, in which a warp factor dimension is introduced; the resulting modifications to the Newtonian interaction in quantum-corrected cosmological settings are discussed in detail. Full article

Wormholes require negative energy, and therefore an exotic matter source. Since Casimir’s energy is negative, it has been speculated as a good candidate to source those objects a long time ago. However, only very recently a full solution for $3+1$ dimensions has been found by Garattini, thus the Casimir energy can be a source of traversable wormholes. We have recently shown that this can be generalized to higher dimensional spacetimes. Lately, Garattini sought to analyze the effects of Yukawa-type terms on shape functions and obtained promising results. However, his approach breaks down the usual relation between the energy density and the radial pressure of the Casimir field. In this work, we study the effects of the same three Yukawa-type corrective factors on the shape function of the Casimir wormhole keeping the usual way to obtain the radial pressure from the energy density. We show that, in addition to being able to construct traversable wormholes that satisfy all the necessary conditions, it is possible to obtain adequate constraints on the constants to recover the standard case with no double limit used by Garatinni. We show that, for some values of the Yukawa parameter, it is possible to generate a repulsive gravitational wormhole. Finally, we analyze the stability of the solutions and find the upper bounds for the Yukawa factor. Full article

In this manuscript, we review the motion of a two-body celestial system (planet–sun) for a Yukawa-type correction on Newton’s gravitational potential using Hamilton’s formulation. We reexamine the stability using the corresponding linearization Jacobian matrix, and verify that the conditions of Bertrand’s theorem are met for radii $\ll {10}^{15}$ m, meaning that bound closed orbits are expected. Applied to the solar system, we present the equation of motion of the planet, then solve it both analytically and numerically. Making use of the analytical expression of the orbit, we estimate the Yukawa strength $\alpha$ and find it to be larger than the nominal value (${10}^{-8}$) adopted in previous studies, in that it is of order ($\alpha ={10}^{-4}-{10}^{-5}$) for the terrestrial planets (Mercury, Venus, earth, Mars, and Pluto) and even larger ($\alpha ={10}^{-3}$) for the giant planets (Jupiter, Saturn, Uranus, and Neptune). Taking the inputs ($r_{min},v_{mas},e$) observed by NASA, we analyse the orbits analytically and numerically for both the estimated and nominal values of $\alpha$ and determine the corresponding trajectories. For each obtained orbit, we recalculate the characterizing parameters ($r_{min},r_{max},a,b,e$) and compare their values according to the potential (Newton with/without Yukawa correction) and method (analytical and/or numerical) used. When compared to the observational data, we conclude that the path correction due to Yukawa correction is on the order of up to 80 million km (20 million km) as the maximum deviation occurring for Neptune (Pluto) for a nominal (estimated) value of $\alpha$. Full article

It has been known that in the nanometer interaction range the available experimental data do not exclude the Yukawa-type corrections to Newton’s gravitational law, which exceed the Newtonian gravitational force by many orders of magnitude. The strongest constraints on the parameters of Yukawa-type interaction in this interaction range follow from the experiments on neutron scattering and from measurements of the lateral and normal Casimir forces between corrugated surfaces. In this work, we demonstrate that by optimizing the experimental configuration at the expense of the higher corrugation amplitudes and smaller periods of corrugations it is possible to considerably strengthen the currently available constraints within the wide interaction range from 4.5 to 37 nm. We show that the maximum strengthening by more than a factor of 40 is reachable for the interaction range of 19 nm. Full article

We consider axionlike particles as the most probable constituents of dark matter, the Yukawa-type corrections to Newton’s gravitational law and constraints on their parameters following from astrophysics and different laboratory experiments. After a brief discussion of the results by Prof. Yu. N. Gnedin in this field, we turn our attention to the recent experiment on measuring the differential Casimir force between Au-coated surfaces of a sphere and the top and bottom of rectangular trenches. In this experiment, the Casimir force was measured over an unusually wide separation region from 0.2 to $8\mathsf{\mu }$m and compared with the exact theory based on first principles of quantum electrodynamics at nonzero temperature. We use the measure of agreement between experiment and theory to obtain the constraints on the coupling constant of axionlike particles to nucleons and on the interaction strength of a Yukawa-type interaction. The constraints obtained on the axion-to-nucleon coupling constant and on the strength of a Yukawa interaction are stronger by factors of 4 and 24, respectively, than those found previously from gravitational experiments and measurements of the Casimir force but weaker than the constraints following from a differential measurement where the Casimir force was nullified. Some other already performed and planned experiments aimed at searching for axions and non-Newtonian gravity are discussed, and their prospects are evaluated. Full article

Constraints on the Yukawa-type corrections to Newton’s gravitational law and on the coupling constant of axionlike particles to nucleons obtained from different laboratory experiments are reviewed and compared. The constraints on non-Newtonian gravity under discussion cover the wide interaction range from nanometers to millimeters and follow from the experiments on neutron scattering, measuring the Casimir force and Cavendish-type experiments. The constraints on the axion-to-nucleon coupling constant following from the magnetometer measurements, Cavendish-type experiments, Casimir physics, and experiments with beams of molecular hydrogen are considered, which refer to the region of axion masses from ${10}^{-10}$ to 200 eV. Particular attention is given to the recent constraints obtained from measuring the Casimir force at nanometer separation distance between the test bodies. Several proposed experiments focussed on constraining the non-Newtonian gravity, axionlike particles and other hypothetical weakly interacting particles, such as chameleons and symmetrons, are discussed. Full article