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On bianchi type-I vacuum solutions inR+R 2 theories of gravitation. I. The isotropic case

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Abstract

From a LagrangianL= (1/κ)(-g)1/2[R/2+l2(αR ik R ik+βR 2)] one obtains fourth-order field equations for the metrical tensorg ik. Inserting a 3-flat Robertson-Walker line element, the set of their vacuum solutions will be enumerated completely. The qualitative behavior, and especially the influence of thel 2-terms (which is possibly necessary for the renormalization of quantum gravity) in certain stages of evolution follow from a phase plane analysis. Depending on the sign of coupling, one obtains either exponentially increasing or oscillating solutions at late times as well as special solutions without an initial singularity.

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  1. Zentralinstitut für Astrophysik, Akademie der Wissenschaften der DDR, Rosa-Luxemburg-Str. 17a, 1502, Potsdam-Babelsberg, Democratic Republic of Germany

    V. Müller & H. -J. Schmidt

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  1. V. Müller
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  2. H. -J. Schmidt
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Müller, V., Schmidt, H.J. On bianchi type-I vacuum solutions inR+R 2 theories of gravitation. I. The isotropic case. Gen Relat Gravit 17, 769–781 (1985). https://doi.org/10.1007/BF00762626

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