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PreprintVersionThe search for non-Newtonian forces has been pursued following many different paths. Recently it was suggested that hypothetical chameleon interactions, which might explain the mechanisms behind dark energy, could be detected in a high-precision force measurement. In such an experiment, interactions between parallel plates kept at constant separation could be measured as a function of the pressure of an ambient gas, thereby identifying chameleon interactions by their unique inverse dependence on the local mass density. During the past years we have been developing a new kind of setup complying with the high requirements of the proposed experiment. In this article we present the first and most important part of this setup -the force sensor. We discuss its design, fabrication, and characterization. From the results of the latter we derive limits on chameleon interaction parameters that could be set by the forthcoming experiment. Finally, we describe the opportunity to use the same setup to measure Casimir forces at large surface separations with unprecedented accuracy, thereby potentially giving unambiguous answers to long standing open questions.

When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on fourdimensional Euclidean Groenewold-Moyal deformed space, also known as 'θ-deformed space' R 4 θ . In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.

We propose a test on the role of relaxation properties of conduction electrons in the Casimir pressure between two parallel metal-coated plates kept at different temperatures. It is shown that for sufficiently thick metallic coatings the Casimir pressure and pressure gradient are determined by the mean of the equilibrium contributions calculated at temperatures of the two plates and by the term independent on separation. Numerical computations of the nonequilibrium pressures are performed for two parallel Au plates of finite thickness as a function of separation and temperature of one of the plates using the plasma and Drude models for extrapolation of the optical data of Au to low frequencies. The obtained results essentially depend on the extrapolation used.Modifications of the CANNEX setup, originally developed to measure the Casimir pressure and pressure gradient in thermal equilibrium, are suggested, which allow different temperatures of one of the plates. Computations of the nonequilibrium pressure and pressure gradient are performed for a realistic experimental configuration. According to our results, even with only a 10 K difference in temperature between the plates, the experiment could discriminate between different theoretical predictions for the total pressure and its gradient, as well as for the contributions to them due to nonequilibrium, at high confidence.

In this paper we discuss one-loop results for the translation invariant non-commutative gauge field model we recently introduced in ref. [1]. This model relies on the addition of some carefully chosen extra terms in the action which mix long and short scales in order to circumvent the infamous UV/IR mixing, and were motivated by the renormalizable non-commutative scalar model of Gurau et al. [2].

In this paper we elaborate on the translation-invariant renormalizable φ 4 theory in 4-dimensional non-commutative space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model. The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.

PreprintVersionWe consider the Cannex (Casimir And Non-Newtonian force EXperiment) test of the quantum vacuum intended for measuring the gradient of the Casimir pressure between two flat parallel plates at large separations and constraining parameters of the chameleon model of dark energy in cosmology. A modification of the measurement scheme is proposed that allows simultaneous measurements of both the Casimir pressure and its gradient in one experiment. It is shown that with several improvements the Cannex test will be capable to strengthen the constraints on the parameters of the Yukawa-type interaction by up to an order of magnitude over a wide interaction range. The constraints on the coupling constants between nucleons and axion-like particles, which are considered as the most probable constituents of dark matter, could also be strengthened over a region of axion masses from 1 to 100 meV.collaboration. On the background of Casimir forces, one could also search for axions and other axion-like particles [13][14][15][16][17][18][19][20] which are considered as hypothetical constituents of dark matter. It is remarkable that taken together, dark energy and dark matter contribute for more than 95% of the energy of the Universe, leaving less than 5% to the forms of energy we are presently capable to observe directly [6].Precise measurements of the Casimir force revealed a problem that the experimental data agree with theoretical predictions of the fundamental Lifshitz theory only under the condition that in calculations one disregards the relaxation properties of conduction electrons and the conductivity at a constant current for metallic and dielectric boundary surfaces, respectively (see review in [5,21] and more modern experiments [22][23][24][25][26][27]). Theoretically, it was shown that an inclusion of the relaxation properties of conduction electrons and the conductivity at a constant current in computations results in a violation of the Nernst heat theorem for the Casimir entropy (see review in [5,21] and further results [28][29][30][31]). Taking into account that both the relaxation properties of conduction electrons for metals and the conductivity at a constant current for dielectrics are well studied really existing phenomena, there must be profound physical reasons for disregarding them in calculations of the Casimir force caused by the zero-point and thermal fluctuations of the electromagnetic field.All precise experiments on measuring the Casimir interaction mentioned above have been performed in the sphere-plate geometry at surface separations below a micrometer. In this paper, we consider the Cannex (Casimir And Non-Newtonian force EXperiment) that was designed to test the quantum vacuum in the configuration of two parallel plates at separations up to 15 µm [32,33]. In addition to the already discussed possibility of testing the nature of dark energy [32], we consider here the potentialities of this experiment for searching thermal effects in the Casimir force, stronger constraints on Yukawa-type c...

Based on our recent findings regarding (non-)renormalizability of non-commutative U⋆(1) gauge theories [1, 2] we present the construction of a new type of model. By introducing a soft-breaking term in such a way that only the bilinear part of the action is modified, no interaction between the gauge sector and auxiliary fields occurs. Demanding in addition that the latter form BRST doublet structures, this leads to a minimally altered non-commutative U⋆(1) gauge model featuring an IR damping behavior. Moreover, the new breaking term is shown to provide the necessary structure in order to absorb the inevitable quadratic IR divergences appearing at one-loop level in theories of this kind. In this paper we compute Feynman rules, symmetries and results for the vacuum polarization together with the one-loop renormalization of the gauge boson propagator and three-point functions.