Abstract:
We construct exact solutions to Einstein equations which represent relativistic disks immersed into an expanding FRW Universe. It is shown that the expansion influences dynamical characteristics of the disks such as rotational curves, surface mass density, etc. The effects of the expansion is exemplified with non-static generalizations of Kuzmin-Curzon and generalized Schwarzschild disks.

Abstract:
We argue that the total number of distinguishable locally Friedmann universes generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e^{e^{3 N}}, where N is the number of e-folds of slow-roll post-eternal inflation. For simplest models of chaotic inflation, N is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant \Lambda the number of distinguishable universes is bounded by e^{|\Lambda|^{-3/4}}. In the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape. We discuss the possibility that the strongest constraint on the number of distinguishable universes may be related not to the properties of the multiverse but to the properties of observers.

Abstract:
We show that the use of suitable theorems for black hole formation in Friedmann expanding universes leads to a modification of the Bekenstein-Hawking entropy. By adopting an argument similar to the original Bekenstein one, we write down the expression for the Bekenstein-Hawking entropy suitable for non-static isotropic expanding universes together with the equation of state of a black hole. This equation can be put in a form similar to the one of an ideal gas but with a factor depending on the Hubble radius. Moreover, we give some argument on a possible relation between our entropy expression and the Cardy-Verlinde one. Finally, we explore the possibility that primordial inflation is due to black hole evaporation in our context.

Abstract:
We discuss the possibility of quantum transitions from the string perturbative vacuum to cosmological configurations characterized by isotropic contraction and decreasing dilaton. When the dilaton potential preserves the sign of the Hubble factor throughout the evolution, such transitions can be represented as an anti-tunnelling of the Wheeler--De Witt wave function in minisuperspace or, in a third-quantization language, as the production of pairs of universes out of the vacuum.

Abstract:
We show that generic anisotropic universes arbitrarily close to the open Friedmann universe allow information processing to continue into the infinite future if there is no cosmological constant or stable gravitationally repulsive stress, and the spatial topology is non-compact. An infinite amount of information can be processed by ``civilisations'' who harness the temperature gradients created by gravitational tidal energy. These gradients are driven by the gravitational waves that sustain the expansion shear and three-curvature anisotropy.

Abstract:
Formulae are presented for the linear growth factor D/a and its logarithmic derivative dlnD/dlna in expanding Friedmann-Robertson-Walker Universes with arbitrary matter and vacuum densities. The formulae permit rapid and stable numerical evaluation. A fortran program is available at http://casa.colorado.edu/~ajsh/growl/ .

Abstract:
We present the Green's functions that are the solutions of the massive Klein-Gordon equation for a scalar field with non-minimal coupling to gravitation for several static and expanding cosmological models. An important feature of such functions is that they can be used to study the appearence of a Casimir energy in models of the universe with compact spatial sections.

Abstract:
The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic Universes is discussed in the context of f(R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the Universe.

Abstract:
We study cosmological perturbations produced by the most general two-derivative actions involving two scalar fields, coupled to Einstein gravity, with an arbitrary field space metric, that admit scaling solutions. For contracting universes, we show that scale-invariant adiabatic perturbations can be produced continuously as modes leave the horizon for any equation of state parameter $w \ge 0$. The corresponding background solutions are unstable, which we argue is a universal feature of contracting models that yield scale-invariant spectra. For expanding universes, we find that nearly scale-invariant adiabatic perturbation spectra can only be produced for $w \approx -1$, and that the corresponding scaling solutions are attractors. The presence of a nontrivial metric on field space is a crucial ingredient in our results.

Abstract:
Solutions analogous to the Weber-Wheeler cylindrical pulse waves are found for the case of cylindrical gravitational waves in an expanding universe. These pulse solutions mimic the asymptotic properties of waves from an isolated source in three dimensions and can be used to test the far-field behavior of numerical simulation techniques.