Seminar of Theoretical Physics - Orchidea Maria Lecian (5.12.2017)
Tuesday 5.12.2017 at 14:00, Lecture room F2/125
Orchidea Maria Lecian:
Analytical expressions for the generic cosmological solution: the limits to the Bianchi solutions
Abstract:
Analytical expressions for the generic cosmological solution for the limits to the Bianchi solutions are found. The most general solution to the Einstein field equations is examined with respect to the space induced by the resolution of the Hamiltonian constraint. Such an n induced space admits the most general generic spherical angular coordinates parametrization, for which the induced (Misner) plane containing the general cosmological solution is considered. The de-homogenization techniques to retrieve on the Misner plane the Bianchi cosmological solution are examined. The analysis of the degrees of freedom needed to evaluate the variance is re-conducted to that concerning the isotropic-volume-growth degrees of freedom, which define a variance for the statistical distribution of Bianchi sequences by the anisotropic degrees of freedom. Bianchi solutions are analyzed and described within this framework. The statistical analyses for the initial conditions for the Bianchi models found for the generic cosmological solutions are commented within the statistical analysis required in the de-homogenization scheme, within which the newly defined parameters are also taken into account. Numerical examples are given, and the paradigms in the application of the proper order algorithm is explained.