I report on some work in progress on the dynamics of extended objects in field theories after a rapid phase transition, as is relevant in the early Universe. An analytic technique, originally introduced to approximate the dynamics of topological defects in condensed matter systems, is extended to cover relativistic objects. An exact formula for the area density of domain walls in D dimensions i...

This is a brief review on the work done recently. It is shown that the global constraints of Gauss’ law ensure that the vacuum angle must be quantized in gauge theories with magnetic monopoles. Our quantization rule is given as θ = 0, or θ = 2πN/n (n 6= 0) with integer n being the relevant topological charge of the magnetic monopole and N is an unfixed integer in this approach. This theoretical...

A widespread myth asserts that all small universe models suppress the CMB quadrupole. In actual fact, some models suppress the quadrupole while others elevate it, according to whether their low-order modes are weak or strong relative to their high-order modes. Elementary geometrical reasoning shows that the low-order modes tend to be relatively weak in well-proportioned spaces (spaces whose dim...

Topological groups whose underlying spaces are basically disconnected, F-, or F′-spaces but not P-spaces considered. It is proved, in particular, that the existence of a Lindelöf disconnected topological group which P-space equivalent to Boolean countable pseudocharacter, free and Abelian zero-dimensional non-P-spaces never F′-spaces, F′-group selective ultrafilters on ω.

We explore the effect of pressure on the electronic properties of the ferromagnetic Mott-Hubbard insulator YTiO3. We show that the pressure-induced insulator-metal transition is accompanied by anisotropic structural changes driven by the competition between strongly orbital dependent one-electron hopping and strong, multiorbital electronic correlations in the real crystal structure of YTiO3. Ou...