Attractor states and infrared scaling in de Sitter space - art. no. 124019

The renormalized expectation value of the energy-momentum tensor for a scal ar field with any mass m and curvature coupling xi is studied for an arbitr ary homogeneous and isotropic physical initial state in de Sitter spacetime . We prove quite generally that (T-ab) has a fixed point attractor behavior at late times, which depends only on m and xi, for any fourth order adiaba tic state that is infrared finite. Specifically, when m(2)+xiR>0, (T-ab) ap proaches the Bunch-Davies de Sitter invariant value at late times, independ ently of the initial state. When m = xi = 0, it approaches instead the de S itter invariant Allen-Folacci value. When m = 0 and xi greater than or equa l to0 we show that the state independent asymptotic value of the energy-mom entum tensor is proportional to the conserved geometrical tensor H-(3)(ab), which is related to the behavior of the quantum effective action of the sc alar field under global Weyl rescaling. This relationship serves to general ize the definition of the trace anomaly in the infrared for massless, nonco nformal fields. In the case m(2) + xiR = 0, but m and xi separately differe nt from zero, (T-ab) grows linearly with cosmic time at late times. For mos t values of m(2) and xi in the tachyonic cases, m(2) + xiR<0, (T-ab) grows exponentially at late cosmic times for all physically admissible initial st ates.