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

Abstract

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.

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

References in corpus (1)

• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem

Cited by in corpus (24)

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• Junction Conditions in f(R) Theories of Gravity
• Some remarks on the dynamical systems approach to fourth order gravity
• Static Solutions for 4th order gravity
• The Cauchy problem of f(R) gravity
• Gödel-type universes in f(R) gravity
• Motion of test bodies in theories with nonminimal coupling
• 6+1 lessons from f(R) gravity
• f(R) gravity: successes and challenges
• Massive Gravity with Mass Term in Three Dimensions
• Perihelion precession for modified Newtonian gravity
• Scalar field mass in generalized gravity
• Inflation with a Weyl term, or ghosts at work
• Gauss-Bonnet lagrangian G ln G and cosmological exact solutions
• Some exact solutions with torsion in 5-D Einstein-Gauss-Bonnet gravity
• Position and frequency shifts induced by massive modes of the gravitational wave background in alternative gravity
• Implications of non-analytical f(R) gravity at Solar-System scales
• Spontaneous breaking of conformal invariance, solitons and gravitational waves in theories of conformally invariant gravitation
• Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole
• Extension of the EGS theorem to metric and Palatini f(R) gravity
• Tensor Potential Description of Matter and Space, III. Gravitation