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Expanding AdSs branes: time dependenteigenvalue problem and production of particles // Tomsk State Pedagogical University Bulletin. 2004. Issue 7 (44). P. 45-49

An analysts is first given of the situation where a scafar field is contained between two fixed, spatially flat, branes. The usual fine-tuning (RS) condition is relaxed, and the branes are allowed to possess a positive effective cosmological constant ». We first analyze the eigenvalue problem for the Kaluza-Klein masses when the metric is time dependent, and consider in detail the case when » is small. Thereafter we consider, in the case of one single brane, the opposite limit in which » is large, acting in a brief period of time T, and present a "sudden approximation" calculation of the energy produced on the brane by the rapidly expanding de Sitter space during this period.