Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-09-02
Theor.Math.Phys. 140 (2004) 1095-1108; Teor.Mat.Fiz. 140 (2004) 241-255
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LATEX, 21 pages, no figure
Scientific paper
We consider a scalar field with a Gauss-Bonnet-type coupling to the curvature in a curved space-time. For such a quadratic coupling to the curvature, the metric energy-momentum tensor does not contain derivatives of the metric of orders greater than two. We obtain the metric energy-momentum tensor and find the geometric structure of the first three counterterms to the vacuum averages of the energy-momentum tensor for an arbitrary background metric of an N-dimensional space-time. In a homogeneous isotropic space, we obtain the first three counterterms of the n-wave procedure, which allow calculating the renormalized values of the vacuum averages of the energy-momentum tensors in the dimensions N=4,5. Using dimensional regularization, we establish that the geometric structures of the counterterms in the $n$-wave procedure coincide with those in the effective action method.
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