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We formulate a general replica field-theoretic framework for stochastic inflation in which a manifestation of dimensional reduction is found. The scale above which the latter becomes dominant is explicitly calculated. It is found that for a wide class of stochastic systems considerable changes of the spectral index inevitably occur on super-horizon scales. We work out an explicit relation between the noise correlator and the non-Gaussianity parameter $f_{NL}$, which thus can effectively be generated entirely by quantum fluctuations.

I describe a variety of bubbles of nothing which do not require a Kaluza-Klein circle but instead may be found in asymptotically flat or AdS spaces without any identifications.  There are many such bubbles which expand outwards and threaten to destabilize spacetimes with more than four dimensions.   In the AdS case, one can show there are both bubbles and topologically trivial smooth states which violate all of the energy bounds, both classical and quantum, in the corresponding gauge theory.

According to Doering and Isham the spectral topos corresponds to any quantum system. The descriptions of the systems become similar to these given by classical theories. Topoi can also modify local smooth spacetime structure. Supposing that a quantum system modifies the local spacetime structure and interacts with a gravitational field via the spectral topos, a natural pattern for non-gravitating quantum zero-point modes of the system, appears. A way how to add gravity into the spectral topos of a system is presented.

Searches for neutrinoless double beta decays could determine if neutrinos are Majorana particles and could measure their absolute mass scale. The initial stage of the Enriched Xenon Observatory project, EXO-200, will look for two-neutrino and neutrinoless double-beta decays of Xe-136 in a liquid-xenon time-projection chamber. By combining the ionization signal with detection of the scintillation light collected in Large Area Avalanche Photodiodes (LAAPDs), an energy resolution of about 1.4% at the decay energy can be achieved.