“Critical” Cosmology in Higher Order Gravity

Mathematical problems in higher order gravity and cosmology

We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of relevance to quantum theory. We discuss the physicality issue arising as a consequence of the conformal transformation theorem, the question of formulating a co...

Stochastic Gravity and Self-Organized Critical Cosmology

A stochastic theory of gravity is described in which the metric tensor is a random variable such that the spacetime manifold is a fluctuating physical system at a certain length scale. A general formalism is described for calculating probability densities for gravitational phenomena in a generalization of general relativity (GR), which reduces to classical GR when the magnitude of the metric fl...

Symmetries of higher-order string gravity actions

In this paper we explicitly prove the invariance of the time-dependent string gravity Lagrangian with up to four derivatives under the global O(d, d) symmetry. CERN-TH/96-291 October 1996 Partially supported by a Polish KBN grant. Permanent address: Institute for Theoretical Physics, Hoża 69, 00-689 Warszawa, Poland. E-mail: [email protected]

Introduction to Higher Order Spatial Statistics in Cosmology

Fourth Order Gravity: Equations, History, and Applications to Cosmology *

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 par...