Fourth order gravity: equations, history, and applications to cosmology

Details Fourth order gravity: equations, history, and applications to cosmology Fourth order gravity: equations, history, and applications to cosmology

2006-02-05

arxiv.org/abs/gr-qc/0602017v2

ECONFC0602061:12,2006; Int.J.Geom.Meth.Mod.Phys.4:209-248,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

51 pages, LaTeX, no figure, lecture for 42nd Karpacz Winter School 6.-11.2.06, references 99-109 and related comments are adde

Scientific paper

10.1142/S0219887807001977

The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented.

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