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.Comment: 29 pages. The previous version is divided in two separate papers. The first four chapters, expanded and modified, form the present paper. The title and abstract are adequately modified, some recent references added. The main conclusions remain unchanged. The second part will also appear in Class. Qu. Gra

Globally maximal timelike geodesics in static spherically symmetric spacetimes: radial geodesics in static spacetimes and arbitrary geodesic curves in ultrastatic spacetimes

This work deals with intersection points: conjugate points and cut points, of timelike geodesics emanating from a common initial point in special spacetimes. The paper contains three results. First, it is shown that radial timelike geodesics in static spherically symmetric spacetimes are globally maximal (have no cut points) in adequate domains. Second, in one of ultrastatic spherically symmetric spacetimes, Morris--Thorne wormhole, it is found which geodesics have cut points (and these must coincide with conjugate points) and which ones are globally maximal on their entire segments. This result, concerning all timelike geodesics of the wormhole, is the core of the work. The third outcome deals with the astonishing feature of all ultrastatic spacetimes: they provide a coordinate system which faithfully imitates the dynamical properties of the inertial reference frame. We precisely formulate these similarities.Comment: 16 pages, 1 figur

Symmetry properties of the metric energy-momentum tensor in classical field theories and gravity

We derive a generic identity which holds for the metric (i.e. variational) energy-momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy-momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime. In this sense a field theory in flat spacetime is not self-contained. When the identity is applied to the gauge invariant spin-two field in Minkowski space, we obtain an alternative and direct derivation of a known no-go theorem: a linear gauge invariant spin-2 field, which is dynamically equivalent to linearized General Relativity, cannot have a gauge invariant metric energy-momentum tensor. This implies that attempts to define the notion of gravitational energy density in terms of the metric energy--momentum tensor in a field-theoretical formulation of gravity must fail.Comment: Revised version to match the published version in Class. Quantum Gra