ar X iv : g r - qc / 0 11 11 09 v 1 3 0 N ov 2 00 1 Null Energy Condition Violations in Eternal Inflation ∗ Serge

The usual scenario of “eternal inflation” involves an approximately de Sitter spacetime undergoing upward fluctuations of the local expansion rate H. This spacetime requires frequent violations of the Null Energy Condition (NEC). We investigate the fluctuations of the energy-momentum tensor of the scalar field in de Sitter space as a possible source of such violations. We find that fluctuations of the energy-momentum tensor smeared in space and time are well-defined and may provide the NEC violations. Our results for slow-roll inflation are consistent with the standard calculations of inflationary density fluctuations. In the diffusive regime where quantum fluctuations dominate the slow-roll evolution, the magnitude of smeared energymomentum tensor fluctuations is large enough to create frequent NEC violations. The usual picture of eternal inflation [2] involves a locally FRW spacetime which is well described by a de Sitter-like metric with a slowly varying expansion rate H , ds = dt − [a (x, t)] d~x, a (x, t) ≈ e ∫ . (1) ∗Talk given at COSMO-2001, Rovaniemi, Finland, August 29—September 4, 2001. At that time, the author’s affiliation was with the Department of Physics, Case Western Reserve University, 10900 Euclid Ave., Cleveland OH 44106. Based on work in preparation [1].