Energy-momentum tensor of a massless scalar quantum field in a Robertson-Walker universe

P. C.W. Davies, S. A. Fulling, S. M. Christensen, T. S. Bunch

Research output: Contribution to journalArticlepeer-review

124 Scopus citations


The renormalized stress tensor of a free quantum field in a curved space-time should be obtainable by some covariant procedure from the short-distance behavior of the corresponding operator products evaluated at separated points. We perform the covariant expansion of the vacuum expectation value of the point-split stress tensor of a conformally invariant scalar field in a spatially flat Robertson-Walker geometry. When attempting to identify the finite direction-independent part of the coincidence limit of this quantity as the renormalized stress tensor, we encounter ambiguities beyond those corresponding to inevitable renormalizations of coupling constants in the gravitational field equations, but nevertheless limited to local geometrical tensors of fourth order or lower in derivatives of the metric. The ambiguities are resolved by requiring the tensor to be covariantly conserved and to have a trace of the form indicated by recent research on conformal anomalies. Various techniques useful in calculations of this kind are described.

Original languageEnglish (US)
Pages (from-to)108-142
Number of pages35
JournalAnnals of Physics
Issue number1
StatePublished - Nov 1977
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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