Search Results (3)

A new conformally invariant gravitational generalization of the Born–Infeld (BI) model is proposed and analyzed from the point of view of symmetries. Taking a geometric identity involving the determinant functions det$f\left(B_{\mu \nu },F_{\mu \nu }\right)$ with the Bach $B_{\mu \nu }$ and the electromagnetic field $F_{\mu \nu }$ tensors (with the 4-dimensional Greek letter indexes), two characteristic geometrical Lagrangian densities (Lagrangians) are derived: the first Lagrangian being the square root of the determinant function $\sqrt{\left|det\left(B_{\mu \nu }+F_{\mu \nu }\right)\right|}$ (reminiscent of the standard BI model) and the second Lagrangian being the fourth root $\sqrt[4]{gdet\left(B_{\alpha \gamma }{B}_{\beta }^{\gamma }+F_{\alpha \gamma }{F}_{\beta }^{\gamma }\right)}$. It is shown, after explicit computation of the gravitational equations, that the square-root model is incompatible with the inclusion of the electromagnetic tensor, consequently forcing the nullity of $F_{\mu \nu }$. In sharp contrast, the traceless fourth-root model is fully compatible and a natural ansatz of the type $B_{\mu \rho }{B}_{\nu }^{\rho }\propto \mathrm{\Omega }\left(x\right)g_{\mu \nu }$ (conformal-Killing), with $\mathrm{\Omega }$ the conformal factor and x the 4-coordinate, can be considered. Among other essential properties, the geometrical conformal Lagrangian of the fourth-root type is self-similar with respect to the determinant g of the metric tensor $g_{\mu \nu }$ and can be extended to non-Abelian fields in a way similar to the model developed by the author earlier. This self-similarity is related to the conformal properties of the model, such as the Bach currents or flows presumably of a topological origin. Possible applications and comparisons with other models are briefly discussed. Full article

The large-scale dynamics of the universe is generally described in terms of the time-dependent scale factor $a\left(t\right)$. To make contact with observational data, the $a\left(t\right)$ function needs to be related to the observable $z\left(r\right)$ function, redshift versus distance. Model fitting of data has shown that the equation that governs $z\left(r\right)$ needs to contain a constant term, which has been identified as Einstein’s cosmological constant. Here, it is shown that the required constant term is not a cosmological constant but is due to an overlooked geometric difference between proper time t and look-back time $t_{\mathrm{lb}}$ along lines of sight, which fan out isotropically in all directions of the 3D (3-dimensional) space that constitutes the observable universe. The constant term is needed to satisfy the requirement of spatial isotropy in the local limit. Its magnitude is independent of the epoch in which the observer lives and agrees with the value found by model fitting of observational data. Two of the observational consequences of this explanation are examined: an increase in the age of the universe from 13.8 Gyr to 15.4 Gyr, and a resolution of the $H_0$ tension, which restores consistency to cosmological theory. Full article

Within the framework of the XHe hypothesis, the positive results of the DAMA/NaI and DAMA/LIBRA experiments on the direct search for dark matter particles can be explained by the annual modulation of the radiative capture of dark atoms into low-energy bound states with sodium nuclei. Since this effect is not observed in other underground WIMP (weakly interacting massive particle) search experiments, it is necessary to explain these results by investigating the possibility of the existence of low-energy bound states between dark atoms and the nuclei of matter. Numerical modeling is used to solve this problem, since the study of the XHe–nucleus system is a three-body problem and leaves no possibility of an analytical solution. To understand the key properties and patterns underlying the interaction of dark atoms with the nuclei of baryonic matter, we develop the quantum mechanical description of such an interaction. In the numerical quantum mechanical model presented, takes into account the effects of quantum physics, self-consistent electromagnetic interaction, and nuclear attraction. This approach allows us to obtain a numerical model of the interaction between the dark atom and the nucleus of matter and interpret the results of direct experiments on the underground search for dark matter, within the framework of the dark atom hypothesis. Thus, in this paper, for the first time, steps are taken towards a consistent quantum mechanical description of the interaction of dark atoms, with unshielded nuclear attraction, with the nuclei of atoms of matter. The total effective interaction potential of the OHe–Na system has therefore been restored, the shape of which allows for the preservation of the integrity and stability of the dark atom, which is an essential requirement for confirming the validity of the OHe hypothesis. Full article