Том 22, № 1 (2016)

The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum (gravitons) and classical (gravitational waves). We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form a de Sitter state of the empty homogeneous isotropic Universe. This state is an exact solution to the self-consistent equations of finite one-loop quantum gravity for gravitons in the empty FLRW space. It is also an exact solution to the selfconsistent equations of back-reaction for classical gravitational waves in the same space. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to carry out a transition to imaginary time and then to return to real time, which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that time was used as a complex variable, and this fact has a deep but still not understood significance. The de Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start (inflation) and by the end (dark energy) of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10⁻⁵ is produced by fluctuations in the number of gravitons. The existence of a threshold and a unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and de Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w > −1 for inflation and w < −1 for dark energy is consistentwith the observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy.

We study the properties of possible static, spherically symmetric configurations in k-essence theories with the Lagrangian functions of the form F(X), X ≡ ϕ,_αϕ,^α. A no-go theorem has been proved, claiming that a possible black-hole-like Killing horizon of finite radius cannot exist if the function F(X) is required to have a finite derivative dF/dX. Two exact solutions are obtained for special cases of kessence: one for F(X) = F₀X^1/3, another for F(X) = F₀|X|^1/2 − 2Λ, where F₀ and Λ are constants. Both solutions contain horizons, are not asymptotically flat, and provide illustrations for the obtained nogo theorem. The first solution may be interpreted as describing a black hole in an asymptotically singular space-time, while in the second solution two horizons of infinite area are connected by a wormhole.

Flat Friedmann cosmologies with stiff fluid are considered in the framework of the Einstein–Cartan theory. The version of this theory which simultaneously takes into consideration two sources of torsion, namely, a perfect fluid with the vacuum equation of state and a nonminimally coupled scalar field, is studied. It is demonstrated that, for bouncing models, phantom cosmologies with and without a Big Rip singularity are possible. Singular expanding models are presented where the early stages are dominated by a scalar-torsion field which behaves as an ultrastiff fluid, while the late stages are dominated by a perfect fluid which causes a de Sitter asymptotic. Some cosmological consequences of two sources of torsion are discussed.

Starting from the origin of Einstein’s general relativity (GR), the request of Mach on the theory’s structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of the Equivalence Principle (EP). TheMOND theory byMilgrom proposes a modification of Newtonian dynamics, and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a nongeodesic ratio m_i/m_g can be fixed and that Milgrom’s acceleration is retrieved at low energies.

In the dynamics of three-dimensional space in global time, the global scale takes the form of a discrete variable whose dynamics is described by Friedmann models. Due to a nonzero Hamiltonian, a differential equation is formed for a vacuum configuration. This equation has exact discrete solutions with the spectrum ε_n = ±\(\sqrt {2n} \). Three Hilbert spaces are connected with this equation. We study the dynamics of wave packets on the basis of a small number of eigenfunctions.