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

By H. Schmidt. 2006

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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 of how within fourth order gravity with L= R + R2, 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/66aaa149062aa1aec3265e3c93d82831a3dea3bb

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Citations in the corpus

f(R) Theories (2010, background): “The readers who are interested in the more detailed history of f (R) theories and fourth-order gravity may have a look at the review articles by Schmidt [531] and Sotiriou and Faraoni [556].”
f(R) Theories Of Gravity (2008, background): “…interest of the scientific community in higher-order theories of gravity, i.e., modifications of the Einstein–Hilbert action in order to include higher-order curvature invariants with respect to the Ricci scalar [see (Schmidt, 2007) for a historical review and a list of references to early work].”
Massive 3D supergravity (2009, background): “heory, and ignoringthe supergravity ‘auxiliary’ ﬁeld S, this is known to be equivalent to a scalar ﬁeld coupled to gravity with a potential that gives the scalar ﬁeld a mass ˜min the linearized limit [25]. This model has never been supersymmetrized, to our knowledge. We shall now consider in turn th”
The Lovelock Black Holes (2008, background): “ ﬁeld redeﬁnition that involves a conformal transformation) to General Relativity coupled to a scalar ﬁeld φ, provided a suitable self-interaction potential 1 V(φ) that depends on the function f (see [4] and references therein). In this sense, these theories are not diﬀerent from particular models o”