Monday, June 12, 2006

More null energy condition


This is an extension of an earlier paper hep-th/0502203 (see blog post here). We show that in a broad class of models violation of the null energy condition indicates instability. The results are relevant to general relativity and to cosmology.

A paper by Dubovsky et al. (Ref. [6] in the new paper) exhibited a loophole in our earlier results involving superluminal (acausal) excitations. We traced this to an equation in our analysis (Eq. (47) in the new paper) that needs to be solved to find the unstable mode. In models with superluminal excitations this equation is solvable in some frames but not others (this is a sickness of acausality). Correspondingly, in some frames the Hamiltonian has no negative mode. In the appendix of the new paper we show that requiring causality is enough to restore the link between NEC violation and instability.

Coincidentally, the paper posted just before ours, hep-th/0606090 (Creminelli et al.) discusses some effective theories that can violate the NEC and be stable. Our results don't cover these models as they have four-derivative terms in the Lagrangian. We restrict ourselves to models which have classical equations of motion that are second order PDEs. I don't know what to make of third and higher order PDEs -- who knows what initial conditions are well-posed in those models.

However, the Creminelli et al. paper and the Dubovsky et al. paper are examples of how the creativity of model builders tends to evade the results of theorem-provers. No go theorems are only as good as their assumptions!

The null energy condition and instability

Authors: Roman V. Buniy, Stephen D. H. Hsu, Brian M. Murray

We extend previous work showing that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. Simple examples are given to illustrate these results. The role of causality in our results is discussed. Finally, we extend the fluid results to more general systems in thermal equilibrium. When applied to the dark energy, our results imply that w is unlikely to be less than -1.

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