A few years ago, Cornish, Spergel and Starkman ͑CSS͒ suggested that a multiply connected ''small'' universe could allow for classical chaotic mixing as a preinflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham ͑DHI͒ calculated the Casimir energy for static multiply connected flat space-times. Because of the interest in small volume hyperbolic universes ͑e.g., CSS͒, we generalize the DHI calculation by making a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static universe, whose spatial sections are the Weeks manifold, the smallest universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.
It is believed that soon after the Planck era, space time should have a
semi-classical nature. According to this, the escape from General Relativity
theory is unavoidable. Two geometric counter-terms are needed to regularize the
divergences which come from the expected value. These counter-terms are
responsible for a higher derivative metric gravitation. Starobinsky idea was
that these higher derivatives could mimic a cosmological constant. In this work
it is considered numerical solutions for general Bianchi I anisotropic
space-times in this higher derivative theory. The approach is ``experimental''
in the sense that there is no attempt to an analytical investigation of the
results. It is shown that for zero cosmological constant $\Lambda=0$, there are
sets of initial conditions which form basins of attraction that asymptote
Minkowski space. The complement of this set of initial conditions form basins
which are attracted to some singular solutions. It is also shown, for a
cosmological constant $\Lambda> 0$ that there are basins of attraction to a
specific de Sitter solution. This result is consistent with Starobinsky's
initial idea. The complement of this set also forms basins that are attracted
to some type of singular solution. Because the singularity is characterized by
curvature scalars, it must be stressed that the basin structure obtained is a
topological invariant, i.e., coordinate independent.Comment: Version accepted for publication in PRD. More references added, a few
modifications and minor correction
In this paper we investigate the past evolution of an anisotropic Bianchi I universe in R + R 2 gravity. Using the dynamical system approach we show that there exists a new two-parameter set of solutions that includes both an isotropic "false radiation" solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behavior of the shear from a specific property of f (R) gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally, we numerically check our results.
The present paper describes the manufacturing process of open-pore metal foams by investment casting and the mesostructural/morphological evolution resulting from a new technique of modifying the precursor. By this technique, the precursor is coated with a polymer layer whereby a thickening of the struts occurs. Relative densities in the range of1.85≤ρrel≤25%of open-pore metal foams can be achieved with high accuracy. The samples investigated have pore densities ofρP=7 ppi, 10 ppi, and 13 ppi. The relevant processing parameters needed for a homogenous formation of the polymer layer are determined for two different coating materials and the resulting open-pore foam’s mesostructure is characterized qualitatively and quantitatively. The alloy used for investment casting open-pore metal foamsis AlZn11. The microstructural evolution of these foams is evaluated as a function of the mesostructure. Differences in the microstructure are observed for foams with low and high relative densities and discussed in terms of cooling subsequent to investment casting.
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