Vol 23, No 3 (2017)

We show that, on the average, a homogeneous and isotropic scalar field and, on the average, homogeneous and isotropic ensembles of classical and quantum gravitational waves generate the de Sitter expansion of empty (with no matter) space-time. At the start and by the end of its cosmological evolution, the Universe is empty. The contemporary Universe is about 70% empty, so the effect of cosmological acceleration should be very noticeable. One can assume that itmanifests itself as dark energy. At the start of the cosmological evolution, before the firstmatter was born, the Universe was also empty. The cosmological acceleration of such empty space-time can manifests itself as inflation. To get the de Sitter accelerated expansion of empty space-time under influence of scalar fields and classical and quantum gravitational waves, one needs to make a mandatory Wick rotation, i.e., one needs to make a transition to Euclidean space of imaginary time. One can assume that the very existence of inflation and dark energy could be considered as a possible observable evidence for the fact that time by its nature could be a complex value which manifests itself precisely at the start and by the end of the evolution of the Universe, i.e., in those periods when the Universe is empty (or nearly empty).

Recently, some authors considered the origin of a type-IV singular bounce in modified gravity and obtained the explicit form of F(R) which can produce this type of cosmology. In this paper, we show that during the contracting branch of type-IV bouncing cosmology, the sign of gravity changes, and antigravity emerges. In our model, M0 branes get together and shape a universe, an anti-universe, and a wormhole which connects them. As time passes, this wormhole is dissolved in the universes, F(R) gravity emerges, and the universe expands. When the brane universes become close to each other, the squared energy of their system becomes negative, and some tachyonic states are produced. To remove these states, universes are assumed to be compact, the sign of compacted gravity changes, and anti-F(R) gravity arises, which causes getting away of the universes from each other. In this theory, a Type-IV singularity occurs at t = t_s, which is the time of producing tachyons between expansion and contraction branches.

Cosmological inflationary models based on a self-interacting scalar field are considered. A slow-roll model is formulated as an optimal control problem. Application of Pontryagin’s maximum principle leads to an exact solution.

The paper presents an analysis of effective potentials of Dirac equations in Schwarzschild and Reissner–Nordström fields. It is shown that in the majority of the explored cases the condition of a particle “fall” to the corresponding event horizons is fulfilled. An exception is one of the solutions with a normalizable wave functions for the Reissner–Nordström extreme field, for which the existence of a stationary bound state of a half-spin particles is possible inside the event horizon.

We apply the formula for quadrupole gravitational loss of Einstein’s linearized theory to calculate the energy loss of an infalling pointlike mass into a black hole in the context of quadratic f(R) gravity.

We construct explicit examples of globally regular static, spherically symmetric solutions of general relativity with a phantom scalar field as the source of gravity, describing traversable wormholes with flat asymptotic regions on both sides of the throat as well as regular black holes, in particular, those called black universes. To explain why such phantom fields are not observed under usual conditions, we invoke the concept of “invisible ghosts,” which means that the phantom field decays quickly enough at infinity and is there too weak to be observed. This approach leads to wormhole models in which the spherical radius is almost constant in some range of the radial coordinate near the throat, forming a “long throat.” We discuss the peculiar features and difficulties of the stability problem for such configurations. It is shown that the limiting case of a “maximally long throat” has the form of an unstable model with the Nariai metric. This allows us to conjecture that a long throat does not stabilize wormholes with a scalar source.

The scalar-tensor theory of gravitation proposed by Mbelek and Lachièze-Rey has been previously shown to lead to a possible explanation of the forces measured in asymmetric resonant microwave cavities. However, in the derivation of the equations from the action principle some inconsistencies were observed, like no need to vary the electromagnetic invariant in a scalar source term. Also, the forces obtained were too high, in view of reconsideration of the experiments originally reported and of newly published results. In the present work, the equations are re-derived using the full variation of the action, and also the constant of the theory re-evaluated employing the condition that no anomalous gravitational effects are produced by the Earth’s magnetic field. It is shown that the equations originally employed were correct, and that the newly evaluated constant gives the correct magnitude for the forces recently reported.