Testing Gravity and Predictions Beyond the Standard Model at Short Distances: The Casimir Effect

The Standard Model of elementary particles and their interactions does not include the gravitational interaction and faces problems in understanding of the dark matter, dark energy, strong CP violation etc. In continuing attempts to solve these problems, many predictions of new light elementary particles and hypothetical interactions beyond the Standard Model have been made. These predictions can be constrained by many means and, specifically, by measuring the Casimir force arising between two closely spaced bodies due to the zero-point and thermal fluctuations of the electromagnetic field. After a brief survey in the theory of the Casimir effect, the strongest constraints on the power-type and Yukawa-type corrections to Newtonian gravity, following from measuring the Casimir force at short distances, are considered. Next,the problems of dark matter, dark energy and their probable constituents are discussed. This is followed by an analysis of constraints on the dark matter particles, and, specifically, on axions and axionlike particles, obtained from the Casimir effect. The question of whether the Casimir effect can be used for constraining the spin-dependent interactions is also considered. Then the constraints on the dark energy particles, like chameleons and symmetrons, are examined. In all cases the subject of our treatment is not only measurements of the Casimir force but some other relevant table-top experiments as well. In conclusion, the prospects of the Casimir effect for constraining theoretical predictions beyond the Standard Model at short distances are summarized.Comment: 40 pages, 5 figure

Casimir Effect Invalidates the Drude Model for Transverse Electric Evanescent Waves

We consider the Casimir pressure between two metallic plates and calculate the four contributions to it determined by the propagating and evanescent waves and by the transverse magnetic and transverse electric polarizations of the electromagnetic field. The range of interplate separations is considered where nearly the whole pressure has its origin in the electromagnetic response of conduction electrons. In the Casimir physics, this response is described either by the dissipative Drude model resulting in contradictions with the measurement data or by the experimentally consistent but dissipationless plasma model. It is shown that the total transverse magnetic contribution to the Casimir pressure due to both the propagating and evanescent waves and the transverse electric contribution due to only the propagating waves, computed by means of the Drude model, correlate well with the corresponding results obtained using the plasma model. The conclusion is made that a disagreement between the theoretical predictions obtained using the Drude model and precision measurements of the Casimir force is not caused by the account of dissipation in itself, but arises from an incorrect description of the response of metals to the low-frequency transverse electric evanescent waves by this model. It is demonstrated that the Drude model has no supporting experimental evidence in the range of transverse electric evanescent waves, so that the above conclusion is consistent with all available information. The alternative test of the Drude model for the transverse electric evanescent waves suggested in the framework of classical electrodynamics is discussed.Comment: 15 pages, 5 figure

Large-Separation Behavior of the Casimir-Polder Force from Real Graphene Sheet Deposited on a Dielectric Substrate

The Casimir-Polder force between atoms or nanoparticles and graphene-coated dielectric substrates is investigated in the region of large separations. Graphene coating with any value of the energy gap and chemical potential is described in the framework of the Dirac model using the formalism of the polarization tensor. It is shown that the Casimir-Polder force from a graphene-coated substrate reaches the limit of large separations at approximately 5.6 $\mu$m distance between an atom or a nanoparticle and graphene coating independently of the values of the energy gap and chemical potential. According to our results, however, the classical limit, where the Casimir-Polder force no longer depends on the Planck constant and the speed of light, may be attained at much larger separations depending on the values of the energy gap and chemical potential. In addition, we have found a simple analytic expression for the Casimir-Polder force from a graphene-coated substrate at large separations and determined the region of its applicability. It is demonstrated that the asymptotic results for the large-separation Casimir-Polder force from a graphene-coated substrate are in better agreement with the results of numerical computations for the graphene sheets with larger chemical potential and smaller energy gap. Possible applications of the obtained results in nanotechnology and bioelectronics are discussed.Comment: 15 pages, 6 figure

Nonequilibrium Casimir-Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap

The Casimir-Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of graphene coating to the electromagnetic field is described on the basis of first principles of quantum electrodynamics at nonzero temperature using the formalism of the polarization tensor in the framework of the Dirac model. The nonequilibrium Casimir-Polder force is calculated as a function of the mass-gap parameter, chemical potential of graphene and temperature of the graphene-coated plate, which can be both higher and lower than that of the environment. It is shown that the force value increases with increasing chemical potential, and this increase is more pronounced when the temperature of a graphene-coated plate is lower than that of the environment. The nonequilibrium force also increases with increasing temperature of the graphene-coated plate. This increase is larger when the plate is hotter than the environment. The effect is revealed that the combined impact of the chemical potential $\mu$ and mass gap $\Delta$ of graphene coating depends on the relationship between $\Delta$ and 2$\mu$. If $2\mu>\Delta$ the magnitude of the nonequilibrium force between nanoparticles and a cooled graphene-coated plate becomes much larger than for a graphene coating with $\mu=0$. The physical reasons explaining this effect are elucidated. Possible applications of the obtained results are discussed.Comment: 22 pages, 7 figure

Impact of Mass-Gap on the Dispersion Interaction of Nanoparticles with Graphene out of Thermal Equilibrium

We consider the nonequilibrium dispersion force acting on nanoparticles on the source side of gapped graphene sheet. Nanoparticles are kept at the environmental temperature, whereas the graphene sheet may be either cooler or hotter than the environment. Calculation of the dispersion force as a function of separation at different values of the mass-gap parameter is performed using the generalization of the fundamental Lifshitz theory to the out-of-thermal-equilibrium conditions. The response of gapped graphene to quantum and thermal fluctuations of the electromagnetic field is described by the polarization tensor in (2+1)-dimensional space-time in the framework of the Dirac model. The explicit expressions for the components of this tensor in the area of evanescent waves are presented. The nontrivial impact of the mass-gap parameter of graphene on the nonequilibrium dispersion force, as compared to the equilibrium one, is determined. It is shown that, unlike the case of a pristine graphene, the nonequilibrium force preserves an attractive character. The possibilities of using the obtained results in the design of micro- and nanodevices incorporating nanoparticles and graphene sheets for their functionality are discussed.Comment: 16 pages, 4 figure

Nonequilibrium Casimir-Polder Interaction Between Nanoparticles and Substrates Coated with Gapped Graphene

The out-of-thermal-equilibrium Casimir-Polder force between nanoparticles and dielectric substrates coated with gapped graphene is considered in the framework of the Dirac model using the formalism of the polarization tensor. This is an example of physical phenomena violating the time-reversal symmetry. After presenting the main points of the used formalism, we calculate two contributions to the Casimir-Polder force acting on a nanoparticle on the source side of a fused silica glass substrate coated with gapped graphene, which is either cooler or hotter than the environment. The total nonequilibrium force magnitudes are computed as a function of separation for different values of the energy gap and compared with those from an uncoated plate and with the equilibrium force in the presence of graphene coating. According to our results, the presence of a substrate increases the magnitude of the nonequlibrium force. The force magnitude becomes larger with higher and smaller with lower temperature of the graphene-coated substrate as compared to the equilibrium force at the environmental temperature. It is shown that with increasing energy gap the magnitude of the nonequilibrium force becomes smaller, and the graphene coating makes a lesser impact on the force acting on a nanoparticle from the uncoated substrate. Possible applications of the obtained results are discussed.Comment: 20 pages, 7 figure

Editorial to the Special Issue “The Casimir Effect: From a Laboratory Table to the Universe”

This Special Issue presents a comprehensive picture of the Casimir effect as a multidisciplinary subject that plays an important role in diversified areas of physics ranging from quantum field theory, atomic physics and condensed matter physics to elementary particle physics, gravitation and cosmology [...

How to Strengthen Constraints on Non-Newtonian Gravity from Measuring the Lateral Casimir Force

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

Centenary of Alexander Friedmann’s Prediction of the Universe Expansion and the Quantum Vacuum

We review the main scientific pictures of the universe developed from ancient times to Albert Einstein and underline that all of them treated the universe as a stationary system with unchanged physical properties. In contrast to this, 100 years ago Alexander Friedmann predicted that the universe expands starting from the point of infinitely large energy density. We briefly discuss the physical meaning of this prediction and its experimental confirmation consisting of the discovery of redshift in the spectra of remote galaxies and relic radiation. After mentioning the horizon problem in the theory of the hot universe, the inflationary model is considered in connection with the concept of quantum vacuum as an alternative to the inflaton field. The accelerated expansion of the universe is discussed as powered by the cosmological constant originating from the quantum vacuum. The conclusion is made that since Alexander Friedmann’s prediction of the universe expansion radically altered our picture of the world in comparison with the previous epochs, his name should be put on a par with the names of Ptolemy and Copernicus

The Nature of Dark Energy and Constraints on Its Hypothetical Constituents from Force Measurements

This review considers the theoretical approaches to the understanding of dark energy, which comprises approximately 68% of the energy of our Universe and explains the acceleration in its expansion. Following a discussion of the main approach based on Einstein’s equations with the cosmological term, the explanations of dark energy using the concept of some kind of scalar field are elucidated. These include the concept of a quintessence and modifications of the general theory of relativity by means of the scalar–tensor gravity exploiting the chameleon, symmetron and environment-dependent dilaton fields and corresponding particles. After mentioning several laboratory experiments allowing us to constrain the hypothetical scalar fields modeling the dark energy, special attention is devoted to the possibility of constraining the parameters of chameleon, symmetron and environment-dependent dilaton fields from measuring the Casimir force. It is concluded that the parameters of each of these fields can be significantly strengthened in near future by using the next-generation setups in preparation suitable for measuring the Casimir force at larger separations