Metric gravity theories and cosmology. I: Physical interpretation and viability

We critically review some concepts underlying current applications of gravity theories with Lagrangians depending on the full Riemann tensor to cosmology. We argue that it is impossible to reconstruct the underlying Lagrangian from the observational data: the Robertson-Walker spacetime is so simple and flexible that any cosmic evolution may be fitted by infinite number of Lagrangians. Confrontation of a solution with the astronomical data is obstructed by the existence of many frames of dynamical variables and the fact that initial data for the gravitational triplet depend on which frame is minimally coupled to ordinary matter. Prior to any application it is necessary to establish physical contents and viability of a given gravity theory. A theory may be viable only if it has a stable ground state. We provide a method of checking the stability and show in eleven examples that it works effectively.

98.80.Jk
04.50.+h
space-time: anti-de Sitter
space-time: de Sitter
ground state: stability
gravitation: nonlinear
energy
expansion: acceleration
space-time: Minkowski
field equations

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