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

TL;DR

This paper explores fourth order gravity theories derived from a Lagrangian L(R), discussing their equations, historical development, and applications to cosmology, including inflation and conformal relations to scalar-tensor theories.

Contribution

It derives and solves the field equations for non-linear L(R) gravity, reviews their historical context, and examines their role in cosmic inflation and conformal transformations.

Findings

Fourth order gravity equations are derived and solved for special cases.

The inflationary phase in R + R^2 gravity acts as a transient attractor.

Conformal relations connect fourth order gravity to scalar-tensor theories.

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.