Abstract:
We study a model of power-law inflationary inflation using the Space-Time-Matter (STM) theory of gravity for a five dimensional (5D) canonical metric that describes an apparent vacuum. In this approach the expansion is governed by a single scalar (neutral) quantum field. In particular, we study the case where the power of expansion of the universe is $p \gg 1$. This kind of model is more successful than others in accounting for galaxy formation.

Abstract:
A simple assumption for dark matter leads to magnetic-monopole-like terms to Maxwell’s Equations, a photon model with wave-particle duality, nuclear stability, a decelerating expansion of the universe, and a dark-matter relativity that defines the origin of space and time.

Abstract:
We develop further the formalism of the non-Abelian gauge field theory on a cell complex space-time and show how the gauge-invariant action and the equations of motion for gauge fields interacting with spinors can be written without a reference to the geometrical nature of the cells of the cell complex. The general results are illustrated with examples of solutions of equations of motion for U(N) and SU(N) gauge groups.

Abstract:
A general formulation of spinor fields in Riemannian space-time is given without using vierbeins. The space-time dependence of the Dirac matrices required by the anticommutation relation {\gamma_{\mu},\gamma_{\nu}}=2g_{\mu\nu} determines the spin connection. The action is invariant under any local spin base transformations in the 32 parameter group Gl(4,c) and not just under local Lorentz transformations. The Dirac equation and the energy-momentum tensor are computed from the action.

Abstract:
It is proven that the usual quadratic general-covariant Lagrangian for the Dirac field leads to a symmetric, divergence-free energy-momentum tensor in the standard Riemannian framework of space-time without torsion, provided the tetrad field components are the only quantities related to gravitation that are varied independently.

Abstract:
Quantum matter in quantum space-time is discussed using general properties of energy-conservation laws. As a rather radical conclusion, it is found that standard methods of differential geometry and quantum field theory on curved space-time are inapplicable in canonical quantum gravity, even at the level of effective equations.

Abstract:
Exotic forms of matter such as carbon nanofoams, hexalambdas, super-hypernuclei, strange stars, pentaquarks, color-balls, etc. and their relations to current problems in cosmo-particle physics such as dark matter and energy are discussed in some details. This is an extended version of the invited talk presented at the International Conference on New Trends in High-Energy Physics , Yalta, Crimea(Ukraine), September 10-17, 2005, which has been published in the Proceedings, edited by P.N.Bogolyubov, P.O.Fedosenko, L.L.Jenkovszky, and Yu.A.Karpenko(Bogolyubov Institute for Theoretical Physics, Kiev, 2005). In an extended and up-dated version of the Chapters I and III, entitled "Exotic Nuclei and Strange Stars", which has been published in Nonlinear Phenomena in Complex Systems 18(2015)25-30, new forms of matter such as exotic nuclei and strange stars are discussed in some detail.

Abstract:
This essay examines our fundamental conceptions of time, spacetime, the asymmetry of time, and the motion of a quantum mechanical particle. The concept of time has multiple meanings and these are often confused in the literature and must be distinguished if any light is to be thrown on this age-old issue. The asymmetry of time also has different meanings that depend on context-although the fundamental time asymmetry is associated with the expansion of the universe. These and related issues are discussed in both classical and quantum mechanical contexts.

Abstract:
We generalize relativistic quantum mechanics and the Standard Model of elementary particle physics by considering a finite limit for the smallest measurable length. The resulting theory of Space-Time Quantization is logically consistent and accounts for all possible particle states by means of four new quantum numbers. They specify possible variations of wave functions at the smallest possible scale in space and time, while states of motion are defined by their large-scale variations. This theory also provides insight into the nature and properties of dark matter particles. It can facilitate their detection and identification because of a very strict conservation law.

Abstract:
Using the Ponce de Leon background metric, which describes a 5D universe in an apparent vacuum: $\bar{G}_{AB}=0$, we study the effective 4D evolution of both, the inflaton and gauge-invariant scalar metric fluctuations, in the recently introduced model of space time matter inflation.