Energy-momentum tensor of particles created in an expanding universe - art. no. 024010

We present a general formulation of the time-dependent initial value proble m for a quantum scalar field of arbitrary mass and curvature coupling in a Friedmann-Robertson-Walker (FRW) cosmological model. We introduce an adiaba tic number basis which has the virtue that the divergent parts of the quant um expectation value of the energy-momentum tensor (T-ab) are isolated in t he vacuum piece of (T-ab), and may be removed using adiabatic subtraction. The resulting renormalized (T-ab) is conserved, independent of the cutoff, and has a physically transparent, quasiclassical form in terms of the avera ge number of created adiabatic "particles." By analyzing the evolution of t he adiabatic particle number in de Sitter spacetime we exhibit the time str ucture of the particle creation process, which can be understood in terms o f the time at which different momentum scales enter the horizon. A numerica l scheme to compute (T-ab) as a function of time with arbitrary adiabatic i nitial states (not necessarily de Sitter invariant) is described. For minim ally coupled, massless fields, at late times the renormalized (T-ab) goes a symptotically to the de Sitter invariant state previously found by Alien an d Folacci, and not to the zero mass limit of the Bunch-Davies vacuum. If th e mass m and the curvature coupling xi differ from zero, but satisfy m(2) xi R = 0, the energy density and pressure of the scalar field grow linearl y in cosmic time demonstrating that, at least in this case, back reaction e ffects become significant and cannot be neglected in de Sitter spacetime.