This award supports research that addresses issues relating to quantum effects in both cosmological and black hole spacetimes. These are questions related to the validity of the semi-classical approximation when it is used to describe the effects of quantized fields on a classical background field and to determine whether observable effects related to the existence of a horizon, in this case a sonic horizon, can be found in certain Bose-Einstein condensates, which can serve as black hole analogues. One project involves determining whether quantum fluctuations in the density and pressure of matter and radiation will be large during a period of inflation when the universe is expanding exponentially. If so, then the semi-classical approximation to gravity breaks down and a different method will be needed to describe what happens. A second project investigates the validity of the semiclassical approximation when the universe contracts for one important model in which the contraction is to a minimal size and is followed by an expansion. Evidence suggesting a quantum instability in this model could indicate that quantum fluctuations become large during the contraction phase. A third project investigates whether quantum effects that could be observed in laboratory studies and which are related to the existence of a horizon exist for a model in which a Bose-Einstein condensate serves as an analog for a black hole. Specifically the density density correlation function is computed in order to determine whether undulations are predicted to occur and whether other new observable effects that require the existence of a horizon can be found.
Completion of these projects will elucidate phenomena ranging from the expansion of the universe to potentially observable effects in black hole analogues. If quantum fluctuations prove to be large in important situations, then predictions made using the semi-classical approximation will be suspect, and a different method must be found to treat the effects of the quantized fields. The work on the validity of the semiclassical approximation could have implications for and be extended to other situations in which this approximation has been used such as the production of particles in the presence of a strong electric field and the modeling of heavy ion collisions in nuclear physics. The work on Bose-Einstein condensates which serve as analog black holes may predict specific effects that experimental condensed matter physicists can attempt to observe in laboratory experiments. If observed, these effects would provide significant evidence that predictions of quantum effects relating to black holes, such as black hole evaporation, are correct. It is expected that at least three undergraduate students and at least one graduate student will participate in many aspects of the research, continuing a long history of the training of students in numerical and analytical research techniques and co-authorship on publications. Results will be disseminated to the research community through publications and presentations at national and international meetings.
