Distances and lensing in cosmological void models

We study the distances and gravitational lensing in spherically symmetric inhomogeneous cosmological models consisting of inner and outer homogeneous regions which are connected by a single shell or double shells at the redshift $z_1 \sim 0.067$. The density and Hubble parameters in the inner region are assumed to be smaller and larger, respectively, than those in the outer region. It is found that at the stage $z_1 < z < 1.5$ the distances from an observer in the inner void-like region are larger than the counterparts (with equal $z$) in the corresponding homogeneous Friedmann models, and hence the magnitudes for the sources at this stage are larger. This effect of the void-like low-density region may explain the deviations of the observed [magnitude-redshift] relation of SNIa from the relation in homogeneous models, independently of the cosmological constant. When the position of the observer deviates from the center, moreover, it is shown that the distances are anisotropic and the images of remote sources are systematically deformed. The above relation at $z \geq 1.0$ and this anisotropy will observationally distinguish the role of the above void-like region from that of the positive cosmological constant. The influence on the time-delay measurement is also discussed.Comment: 14 pages, 11 postscript figures Equation numbers were corrected, Apj 529(2000) No.1 in pres

Classical Analogue of Weak Value in Stochastic Process

One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known symmetrized form of the master equation, which is formally equivalent to the wave equation in quantum mechanics apart from the fact that wave functions are always real. The origin of the unusual behaviors of the weak value such as the negative probability and the abnormal enhancement of some expectations becomes clearer in the present case, where the two-time conditional probability has no ambiguity of imaginary/complex values.Comment: Revised version from Arxiv:1109.4302. To appear in the proceedings of the Symposium on 'Interface between Quantum Information and Statistical Physics', to be published by World Scientifi

Cosmological models with the energy density of random fluctuations and the Hubble-constant problem

First the fluctuation energy is derived from the adiabatic random fluctuations due to the second-order perturbation theory, and the evolutionary relation for it is expressed in the form of rho_f = rho_f (rho), where rho and rho_f are the densities of ordinary dust and the fluctuation energy, respectively. The pressureless matter as a constituent of the universe at the later stage is assumed to consist of ordinary dust and the fluctuation energy. Next, cosmological models including the fluctuation energy as a kind of dark matter are derived using the above relation, and it is found that the Hubble parameter and the other model parameters in the derived models can be consistent with the recent observational values. Moreover, the perturbations of rho and rho_f are studied.Comment: 14 pages, 7 figure

Cosmological entropy production and viscous processes in the (1+3+6)-dimensional space-times

The cosmological entropy production is studied in the (1+3+6)-dimensional space-times consisting of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section). The inner space expands initially and contracts later. First it is shown how the production of the 3-dimensional entropy S_3 within the horizon is strengthened by the dissipation due to viscous processes between the two spaces, in which we consider the viscosity caused by the gravitational-wave transport. Next it is shown under what conditions we can have the critical epoch when S_3 reaches the value 10^{88} in the Guth level and at the same time the outer space is decoupled from the inner space. Moreover, the total entropy S_9 in the 9-dimensional space at the primeval expanding stage is also shown corresponding to S_3.Comment: 21 pages, 13 figure