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We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge-invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctuations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any preexisting cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.
Abramo et al. (1997) studied this question.