@article{0b05f7fb69c4468aa0c3c1040390c836,

title = "Energy-momentum tensor of a massless scalar quantum field in a Robertson-Walker universe",

abstract = "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.",

author = "Davies, {P. C.W.} and Fulling, {S. A.} and Christensen, {S. M.} and Bunch, {T. S.}",

note = "Funding Information: In previous papers [l-7] a renormalized energy-momentum tensor (T,,) has been covariantly defined and explicitly calculated in a variety of concrete two-dimensional models of a quantized scalar field in a curved space-time background. Here this program is extended for the first time to a four-dimensional case, the general Robertson-Walker space-time with Euclidean spacelike sections. This geometry is conformally flat, and we consider here only a conformally coupled masslessf ield, since conformal invariance then permits an exact solution for the normal mode functions and also makes the definition of the vacuum state comparatively unambiguous. We do not, however, make any assumptions about the relation between the renormalized Tuy operators in conformally related space-times, since recent work * Research supported in part by the Science Research Council, Grant B/RG/68807. Preparation of paper supported in part by Texas A & M University, and University of Utah. t Present address: Department of Mathematics, Texas A & M University, College Station, Tex. 77843. 3 Present address: Center for Astrophysics, Harvard University, Cambridge, Mass. 02138. * Present address: Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201.",

year = "1977",

month = nov,

doi = "10.1016/0003-4916(77)90167-1",

language = "English (US)",

volume = "109",

pages = "108--142",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

number = "1",

}