Spinor field in a spherically symmetric Friedmann Universe

In recent years spinor field is being used by many authors to address some burning issues of modern cosmology. The motive behind using the spinor field as a source for gravitational field lies on the fact that the spinor field not only can describe the different era of the evolution but also can simulate different substances such as perfect fluid and dark energy. Moreover, the spinor field is very sensitive to the gravitational one and depending on the gravitational field the spinor field can react differently and change the spacetime geometry and the spinor field itself differently. This paper provides a brief description of the nonlinear spinor field in the FriedmannLemaitre-Robertson-Walker (FLRW) model. The results are compared in Cartesian and spherical coordinates. It is shown that during the transition from Cartesian coordinates to spherical ones, the energy-momentum tensor acquires additional nonzero non-diagonal components that can impose restrictions on either spinor functions or metric ones.

Collapsing Wormholes Sustained by Dustlike Matter

It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is “exotic”—i.e., violates a number of energy conditions. For this reason, it is impossible to construct static wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman’s solution describes the collapsing dust ball; the inner space-time structure of the ball corresponds to the Friedmann universe filled by a dust. In the present work we use the general Tolman’s solution in order to construct a dynamic spherically symmetric wormhole solution in GR with dust-like matter. The solution constructed represents the collapsing dust ball with the inner wormhole space-time structure. It is worth noting that, with the dust-like matter, the ball is made of satisfies the usual energy conditions and cannot prevent the collapse. We discuss in detail the properties of the collapsing dust wormhole.

EoS of Casimir vacuum of massive fields in Friedmann universe

In this paper we study equations of state of Casimir vacuum of massive scalar field and massive bispinor field in compact Friedmann universe. With use of the Abel–Plana formula the renormalization of divergent series for calculation of the quantum means of operators is implemented.

Fifty years of the calculation of the density of particles created in the early Friedmann Universe

The problem of particle creation in cosmology concerning whether the results for the number of particles are infinite or finite is discussed for scalar and spinor particles in Friedmann expanding Universe. It is shown that the results are always finite if one puts in case of scalar particles creation a special term into the Lagrangian. Numerical estimates of the effect of particle creation are made. The role of creation of superheavy particles in cosmology is discussed.

Time in quantum theory, the Wheeler–DeWitt equation and the Born–Oppenheimer approximation

We compare two different approaches to the treatment of the Wheeler–DeWitt (WDW) equation and the introduction of time in quantum cosmology. One approach is based on the gauge-fixing procedure in theories with first-class constraints and the construction of the corresponding Hilbert space of quantum states. The other approach uses the Born–Oppenheimer (BO) method, based on the existence of two energy scales in the model under consideration. We apply both to a very simple cosmological model, including a massless scalar field filling a flat Friedmann universe, and observe that they give similar predictions. We also discuss the problem of time in nonrelativistic quantum mechanics and some questions concerning the correspondence between classical and quantum theories.

Static Casimir condensate of conformal scalar field in Friedmann universe

The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel–Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived.

Cosmic screening of the gravitational interaction

We study a universe filled with cold dark matter in the form of discrete inhomogeneities (e.g. galaxies) and dark energy in the form of a continuous perfect fluid. We develop a first-order scalar perturbation theory in the weak gravity limit around a spatially flat Friedmann universe. Our approach works at all cosmic scales and incorporates linear and nonlinear effects with respect to energy density fluctuations. The gravitational potential can be split into individual contributions from each matter source. Each potential is characterized by a Yukawa interaction with the same range, which is of the order of 3700 Mpc at the present time. The derived equations can form the theoretical basis for numerical simulations for a wide class of modern cosmological models.