We apply the background field method and the effective action formalism to describe the fourdimensional dynamical Casimir effect. Our picture corresponds to the consideration of quantum cosmology for an expanding FRW universe (the boundary conditions act as a moving mirror) filled by a quantum massless GUT which is conformally invariant. We consider cases in which the static Casimir energy is attractive and repulsive. Inserting the simplest possible inertial term, we find, in the adiabatic (and semiclassical) approximation, the dynamical evolution of the scale factor and the dynamical Casimir stress analytically and numerically (for SU (2) super Yang-Mills theory). Alternative kinetic energy terms are explored in the Appendix.

Six-dimensional Einstein-Gauss-Bonnet gravity (with a linear Gauss-Bonnet term) is investigated. This theory is inspired by basic features of results coming from string and M-theory. Dynamical compactification is carried out and it is seen that a four-dimensional accelerating FRW universe is recovered, when the two-dimensional internal space radius shrinks. A nonperturbative structure of the corresponding theory is identified which has either three or one stable fixed points, depending on the Gauss-Bonnet coupling being positive or negative. A much richer structure than in the case of the perturbative regime of the dynamical compactification recently studied by Andrew, Bolen, and Middleton is exhibited. 1. Introduction. To realize that the expansion of the universe is accelerating was one of the most important scientific discoveries of the last century. There are several alternative explanations of this remarkable fact (what already means that it is not well understood yet). A quite appealing possibility for the gravitational origin of the dark energy responsible for this accelerated expansion is the modification of General Relativity (GR) or the corresponding Einsteinian gravity (see [1] for a review of these approaches). Such a well-established and successful theory cannot be modified without a very good reason, and much less in an arbitrary way. But observe that there is no compelling reason why standard GR should be trusted at cosmological scales. For a rather minimal modification of the same, one assumes that the gravitational action might contain some additional terms which would start to grow slowly with decreasing curvature. A particularly interesting formulation is obtained by using well-grounded geometrical arguments, specifically when the modified gravity action is endowed with a function of the Gauss-Bonnet (GB) topological invariant, G, as it was suggested in [2]. It must be noted that different types of dark energy may actually show up in different ways, at large distances. Cold dark matter is known to be localized near galaxy clusters but, quite on the contrary, dark energy distributes uniformly in the universe. The reason for that behavior could be explained by a difference in the equation of state parameter w = p/ρ. Moreover, the effect of gravity on the cosmological fluid turns out to depend on w and it so happens that, even when −1 < w < 0, gravity can act sometimes as a repulsive force. The effect of gravity on matter with −1 < w < 0 can be shown to be opposite to that on usual matter, which becomes dense near a star, while matter with −1 < w < 0 becomes less dense when approaching a star [2]. Dark energy contributes uniformly throughout the universe, which would be indeed consistent, since the equation of state parameter of dark energy is almost −1. If dark energy is of phantom nature (w < −1), its density becomes large near the cluster but if dark energy is of quintessence type (−1 < w < −1/3), then its density becomes smaller. PACSAnother very important argument in favor of the GB ...

Using one-loop effective action in large N and s-wave approximation we discuss the possibility to induce primordial wormholes at the early Universe. An analytical solution is found for self-consistent primordial wormhole with constant radius. Numerical study gives the wormhole solution with increasing throat radius and increasing red-shift function. There is also some indication to the possibility of a topological phase transition. *

Using large N, 4d anomaly induced one-loop effective action for conformally invariant matter (typical GUT multiplet) we study the possibility to induce the primordial spherically symmetric wormholes at the early Universe. The corresponding effective equations are obtained in two different coordinate frames. The numerical investigation of these equations is done for matter content corresponding to N = 4 SU(N) super Yang-Mills theory. For some choice of initial conditions, the induced wormhole solution with increasing throat radius and increasing red-shift function is found.

A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles.