In this work wormholes in viable f (R) gravity models are analyzed. We are interested in exact solutions for stress-energy tensor components depending on different shape and redshift functions. Several solutions of gravitational equations for different f (R) models are examined. The solutions found imply no need for exotic material, while this need is implied in the standard general theory of relativity. A simple expression for weak energy condition (WEC) violation near the throat is derived and analyzed. High curvature regime is also discussed, as well as the question of the highest possible values of the Ricci scalar for which the WEC is not violated near the throat, and corresponding functions are calculated for several models. The approach here differs from the one that has been common since no additional assumptions to simplify the equations have been made, and the functions in f (R) models are not considered to be arbitrary functions, but rather a feature of the theory that has to be evaluated on the basis of consistency with observations for the Solar System and cosmological evolution. Therefore in this work we show that the existence of wormholes without exotic matter is not only possible in simple arbitrary f (R) models, but also in models that are in accordance with empirical data.

In this work the influence of the chiral anomaly effect on the evolution of magnetohydrodynamic turbulence was studied. We argue that before the electroweak symmetry breaking and for temperatures high enough such that the electron mass can be ignored, the description of a charged plasma in general needs to take into account the interplay between turbulence and the anomaly effects. It was demonstrated that this generalization can have important consequences on the evolution of turbulence, leading to the creation of maximally-helical fields from initially non-helical ones. Therefore, chiral effects can strongly support turbulent inverse cascade, and lead to a slower decrease of the magnetic field with time, and also to a faster growth of the correlation length, when compared to the evolution predicted by the standard magnetohydrodynamics description. Using the weak anomaly approximation, and treating the anomaly contributions to magnetic energy and helicity as a small perturbation, we derive the specific solutions for the inverse cascade regime that demonstrate how chiral effects support the inverse cascade.

Motivated by recent proposals of possible wormhole existence in galactic halos, we analyse the cosmological evolution of wormhole solutions in modified f (R) gravity. We construct a dynamical wormhole that asymptotically approaches FLRW universe, with supporting material going to the perfect isotropic fluid described by the equation of state for radiation and matter dominated universe respectively. Our analysis is based on an approximation of a small wormhole -a wormhole that can be treated as matched with the FLRW metric at some radial coordinate much smaller than the Hubble radius, so that cosmological boundary conditions are satisfied. With a special interest in viable wormhole solutions, we refer to the results of reconstruction procedure and use f (R) functions which lead to the experimentally confirmed ΛCDM expansion history of the universe. Solutions we find imply no need for exotic matter near the throat of considered wormholes, while in the limit of f (R) = R this need is always present during radiation and matter dominated epoch.

It is a well known result that the effect of vacuum polarization in gravitational fields will lead to a non-minimal coupling between gravity and electromagnetism. We investigate this phenomenon further by considering the description of static magnetic field around a Schwarzschild black hole. It is found that close to the Schwarzschild horizon the magnetic fields can be strongly modified with respect to both cases of magnetic fields on flat spacetime and magnetic fields minimally coupled on curved spacetime. Under the proper sign of the non-minimal coupling parameter, q, the effective fields can undergo large amplifications. Furthermore, we discuss the physical meaning of the singularities that arise in the considered problem. We conclude by discussing the potential observational effects of vacuum polarization on the magnetic fields. In the case of astrophysical black holes, depending on the value of the coupling parameter, significant modifications of the magnetic near the black hole horizons are possible -which could be used to detect the vacuum polarization effect or at least to put constraints on the values of the coupling parameter. Moreover, we show how the considered effect directly constraints the viability of primordial black holes of sizes smaller than that of the Compton wavelength for the electron, and also impacts the distribution of magnetic fields in the early Universe. arXiv:1809.06054v2 [gr-qc]

Abstract. We analyse solutions of the MHD equations around the electroweak transition taking into account the effects of the chiral anomaly. It is shown that a transition that is not of the first order has direct consequences on the evolution of the asymmetry between leftand right-handed leptons. Assuming an initial chiral asymmetry in the symmetric phase at temperatures higher than the transition temperature, as well as the existence of magnetic fields, it is demonstrated that the asymmetry typically grows with time, until it undergoes a fast decrease at the transition, and then eventually gets damped at lower temperatures in the broken phase. We argue that it is unlikely to have any significant magnetic field amplification as a consequence of the electroweak transition in the Standard model, even when the chiral anomaly is introduced. The presence of a chiral asymmetry between left-and right-handed charge carriers naturally leads to the creation of helical magnetic fields from non-helical fields and this can have consequences on their subsequent evolution. Similarly, an initially vanishing chiral asymmetry is naturally created in the presence of a helical magnetic field.