Finite temperature effective potential on hyperbolic spacetimes.

One major area of research in quantum field theory in curved spacetime in the 1980s has been on interacting quantum fields and their implications ([1, 2], for a review see [3]). The central object of physical interest is the effective potential which should define the dynamics of the early universe at scales bigger than the Planck scale. In particular in new inflationary models [4, 5] the effective cosmological constant is obtained from an effective potential which includes quantum corrections to the classical potential of a scalar field [6]. Unfortunately there are a lot of difficulties in calculating the effective potential or action in a quantum field theory in a general curved spacetime [3]. Only approximations like the derivative expansion in the background field at zero [7, 8, 9] and at finite temperature [10, 11] are available. e-mail: [email protected], [email protected], 37953::cognola 2 Address after October 1, 1993: Department E.C.M., Faculty of Physics, Barcelona University, Diagonal 647, E-08028 Barcelona, Spain e-mail: [email protected], [email protected], 37953::vanzo e-mail: [email protected], [email protected], 37953::zerbini