Confusion in Cosmology and Gravitation

In a series of papers, Santilli and collaborators released various strong statements against the general theory of relativity (GTR) and the standard ΛCDM model of cosmology. In this paper we show that such claims are due to misunderstandings of basic concepts of gravitation and cosmology. In particular, we show that Santilli and collaborators demonstrated neither that the GTR is wrong, nor that the Universe is not expanding. We also show that the so-called iso-gravitation theory (IGT) of Santilli is in macroscopic contrast with geodesic motion and, in turn, with the Equivalence Principle (EP) and must therefore be ultimately rejected. Finally, we show that, although the so called iso-redshift could represent an interesting alternative (similar to the tired light theory historically proposed by Zwicky) to the Universe expansion from a qualitative point of view, it must be rejected from a quantitative point of view because the effect of iso-redshift is 10^?6 smaller than the effect requested to achieve the cosmological redshift.     

Modified General Relativity and Cosmology

Aspects of the modified general relativity theory of Rastall, Al-Rawaf and Taha are discussed in both the radiation- and matter-dominated flat cosmological models. A nucleosynthesis constraint on the theory's free parameter is obtained and the implication for the age of the Universe is discussed. The consistency of the modified matter-dominated model with the neoclassical cosmological tests is demonstrated.     

Non-Archimedean Algebra: Applications to Cosmology and Gravitation

Application of recently developed non-Archimedean algebra to a flat and finite universe of total mass M ₀ and radius R ₀ is described. In this universe, mass m of a body and distance R between two points are bounded from above, i.e., 0mM ₀, 0RR ₀. The universe is characterized by an event horizon at R ₀ (there is nothing beyond it, not even space). The radial distance metric is compressed toward horizon, which is shown to cause the phenomenon of red shift. The corresponding modified Minkowski's metric and Lorentz transforms are obtained. Applications to Newtonian gravity shows a weakening at large scales (RR ₀) and a regular behavior as R0.     

Advanced Mechanics and General Relativity,by J. Franklin

Ion Coulomb crystals, formed by atomic ions at low temperatures in radiofrequency and Penning ion traps, are structures that have remarkable properties and many applications. Images of Coulomb crystals are striking and reveal the crystal structure, which arises from a balance between the trapping forces acting on the ions and their mutual Coulomb repulsion. Applications of these structures range from frequency standards and quantum simulation through to measurement of the cross-sections of chemical reactions of ions.