On particle creation in the flat FRW chart of de Sitter spacetime

The conditions of the Gibbons-Hawking effect, i.e., particle production in the Friedmann-Robertson-Walker chart of the de Sitter spacetime, are revisited. For a theory with a massive scalar and a fermionic field it is shown that, if one considers the Bunch-Davies vacuum state at early times, then only in the case that the condition mc2/H ≫ 1 is fulfilled can one assure that a thermal spectrum of radiation at temperature T = H/2πkB, where kB is the Boltzmann constant, will be obtained at late times. It is pointed out that this important proviso (which is nothing else than the adiabatic condition, as we shall see), is missing in several derivations of this effect in the literature, where the thermal spectrum was obtained without imposing any restriction on the relation between the mass of the field, m and the Hubble constant, H. © 2008 IOP Publishing Ltd.