  We study the renormalized energy-momentum tensor (EMT) of the inflaton
fluctuations in rigid space-times during the slow-rollover regime for chaotic
inflation with a mass term. We use dimensional regularization with adiabatic
subtraction and introduce a novel analytic approximation for the inflaton
fluctuations which is valid during the slow-rollover regime. Using this
approximation we find a scale invariant spectrum for the inflaton fluctuations
in a rigid space-time, and we confirm this result by numerical methods. The
resulting renormalized EMT is covariantly conserved and agrees with the
Allen-Folacci result in the de Sitter limit, when the expansion is exactly
linearly exponential in time. We analytically show that the EMT tensor of the
inflaton fluctuations grows initially in time, but saturates to the value H^2
H(0)^2, where H is the Hubble parameter and H(0) is its value when inflation
has started. This result also implies that the quantum production of light
scalar fields (with mass smaller or equal to the inflaton mass) in this model
of chaotic inflation depends on the duration of inflation and is larger than
the usual result extrapolated from the de Sitter result.
