  We compute the leading order contribution to the stress-energy tensor
corresponding to the modes of a quantum scalar field propagating in a
Friedmann-Robertson-Walker universe with arbitrary coupling to the scalar
curvature, whose exact mode functions can be expanded as an infinite adiabatic
series. While for a massive field this is a good approximation for all modes
when the mass of the field m is larger than the Hubble parameter H, for a
massless field only the subhorizon modes with comoving wave-numbers larger than
some fixed k* obeying k*/a>H can be analyzed in this way. As infinities coming
from adiabatic zero, second and fourth order expressions are removed by
adiabatic regularization, the leading order finite contribution to the
stress-energy tensor is given by the adiabatic order six terms, which we
determine explicitly. For massive and massless modes these have the magnitudes
H^6/m^2 and H^6a^2/k*^2, respectively, and higher order corrections are
suppressed by additional powers of (H/m)^2 and (Ha/k*)^2. When the scale factor
in the conformal time \eta is a simple power a(\eta)=(1/\eta)^n, the
stress-energy tensor obeys P=w\rho with w=(n-2)/n for massive and w=(n-6)/(3n)
for massless modes. In that case, the adiabaticity is eventually lost when
0<n<1 for massive and when 0<n<3/2 for massless fields since in time H/m and
Ha/k* become order one. We discuss the implications of these results for de
Sitter and other cosmologically relevant spaces.
