Abstract:
We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.

Abstract:
We study the quantum vacuum fluctuations around closed Friedmann-Robertson-Walker (FRW) radiation-filled universes with nonvanishing cosmological constant. These vacuum fluctuations are represented by a conformally coupled massive scalar field and are treated in the lowest order of perturbation theory. In the semiclassical approximation, the perturbations are governed by differential equations which, properly linearized, become generalized Lame equations. The wave function thus obtained must satisfy appropriate regularity conditions which ensure its finiteness for every field configuration. We apply these results to asymptotically anti de-Sitter Euclidean wormhole spacetimes and show that there is no catastrophic particle creation in the Euclidean region, which would lead to divergences of the wave function.

Abstract:
We study some collective phenomena that may happen in a multiverse scenario. First, it is posed an interaction scheme between universes whose evolution is dominated by a cosmological constant. As a result of the interaction, the value of the cosmological constant of one of the universes becomes very close to zero at the expense of an increasing value of the cosmological constant of the partner universe. Second, we found normal modes for a 'chain' of interacting universes. The energy spectrum of the multiverse, being this taken as a collective system, splits into a large number of levels, some of which correspond to a value of the cosmological constant very close to zero. We finally point out that the multiverse may be much more than the mere sum of its parts.

Abstract:
We study backreaction in dust universes using exact equations which do not rely on perturbation theory, concentrating on theoretical and observational constraints. In particular, we discuss the recent suggestion (in hep-th/0503117) that superhorizon perturbations could explain present-day accelerated expansion as a useful example which can be ruled out. We note that a backreaction explanation of late-time acceleration will have to involve spatial curvature and subhorizon perturbations.

Abstract:
We study non-degenerate (Petrov type I) silent universes in the presence of a non-vanishing cosmological constant L. In contrast to the L=0 case, for which the orthogonally spatially homogeneous Bianchi type I metrics most likely are the only admissible metrics, solutions are shown to exist when L is positive. The general solution is presented for the case where one of the eigenvalues of the expansion tensor is 0.

Abstract:
It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The particularly interesting case of a mass density, which is cylindrical symmetric in the interior of the dust configuration, is presented. Among other things, this proves the non-existence of homogeneous dust configurations.

Abstract:
Following recent considerations of a non-zero value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi I and Bianchi III universes, with dust and cosmological constant, in order to find out which are physically permitted. In fact, these models undergo isotropisation, except for the Kantowski-Sachs model (Omega_{k_{0}}>0) with Omega_{Lambda_{0}}< Omega_{Lambda_{M}} and for the Bianchi III (Omega_{k_{0}}<0) with Omega_{Lambda_{0}}

Abstract:
We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the Dyer-Roeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to the spatially flat LambdaCDM model.

Abstract:
Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic closed spherical shell filled with fluid are studied. The frequency equation of axially symmetric vibrations for a pervious and an impervious surface is obtained. Free vibrations of a closed spherical shell are studied as a particular case when the fluid is vanished. Frequency as a function of ratio of thickness to inner radius is computed in absence of dissipation for two types of poroelastic materials each for a pervious and an impervious surface. Results of previous works are obtained as a particular case of the present study.

Abstract:
The recently suggested notion of total mass density for closed universes is extended to closed universes with a positive cosmological constant. Assuming that the matter fields satisfy the dominant energy condition, it is shown that the cosmological constant provides a sharp lower bound for the total mass density, and that the total mass density takes this as its minimum value if and only if the spacetime is locally isometric with the de Sitter spacetime. This notion of total mass density is extensible to non-compact three-spaces of homogeneity of Bianchi class A cosmological spacetimes.