Cosmology with Curvature-Saturated Gravitational Lagrangian R/\sqrt{1 + l^4 R^2}

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dc.creatorKleinert, Hagen
dc.creatorSchmidt, Hans-Jürgen
dc.date2000-06-21
dc.date2000-09-19
dc.date.accessioned2026-07-07T03:25:06Z
dc.date.available2026-07-07T03:25:06Z
dc.descriptionWe argue that the Lagrangian for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert Lagrangian L_EH = R /16 pi G and a pure cosmological constant for large R with the curvature-saturated ansatz L_cs=L_EH/ \sqrt{1+l^4 R^2}, where l is a length parameter expected to be a few orders of magnitude above the Planck length. The curvature-dependent effective gravitational constant defined by dL/dR = 1/16 pi G_eff is G_eff = G \sqrt{1+l^4 R^2}^{3}, and tends to infinity for large $R$, in contrast to most other approaches where G_eff-> 0. The theory possesses neither ghosts nor tachyons. In a curvature-saturated cosmology, the coordinates with ds^2 = a^2 [da^2/B(a) - dx^2 - dy^2- dz^2] are most convenient since the curvature scalar becomes a linear function of $B(a)$. Solutions with a big-bang singularity have a much milder behavior of the curvature than in Einstein's theory. In synchronized time, the metric is given by ds^2 = dt^2 - t^{6/5(dx^2 + dy^2+ dz^2). On the technical side we show that two different conformal transformations make L_cs asymptotically equivalent to the Gurovich-ansatz L= | R |^{4/3} on the one hand, and to Einstein's theory with a minimally coupled scalar field with self-interaction on the other.
dc.descriptionAuthor Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/kleiner_re311/preprint.html
dc.identifierhttps://arxiv.org/abs/gr-qc/0006074
dc.identifierhttp://arxiv.org/abs/gr-qc/0006074
dc.identifierGen.Rel.Grav. 34 (2002) 1295-1318
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/33582
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleCosmology with Curvature-Saturated Gravitational Lagrangian R/\sqrt{1 + l^4 R^2}
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