37. Artur Janda
On Lie Symmetries of Certain Spherically Symmetric Systems in General Relativity
Acta Phys. Pol., B , vol. 38, pp. 3961-3969 (2007).
[abstract] [journal] [http://th-www.if.uj.edu.pl/acta/vol38/pdf/v38p3961.pdf]
Certain aspects of Lie-point symmetries in spherically symmetric systems of gravitational physics. Lie symmetries are helpful in solving differential equations. General concepts and a few examples are given: perfect fluid in shearfree motion, the conformal Weyl theory and a higher derivative gravity which is equivalent to General Relativity coupled to certain nonlinear spin-2 field theory.
38. Jacek Guzik, Gary Bernstein, Robert E. Smith
Systematic effects in the sound horizon scale measurements
MNRAS, vol. 375, pp. 1329-1337 (2007).
39. Leszek M. Sokołowski
Metric gravity theories and cosmology: I. Physical interpretation and viability.
Class. Quantum Grav., vol. 24, pp. 3391-3411 (2007).
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.
40. Leszek M. Sokołowski
Metric gravity theories and cosmology: II. Stability of a ground state in f(R) theories.
Class. Quantum Grav., vol. 24, pp. 3713-3734 (2007).
A fundamental criterion of viability of any gravity theory is existence of a stable ground-state solution being either Minkowski, dS or AdS space. Stability of the ground state is independent of which frame is physical. In general, a given theory has multiple ground states and splits into independent physical sectors. All metric gravity theories with the Lagrangian being a function of Ricci tensor are dynamically equivalent to Einstein gravity with a source and this allows us to study the stability problem using methods developed in GR. We apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians the stability criterion works simply and effectively whenever the curvature of the ground state is determined. An infinite number of gravity theories have a stable ground state and further viability criteria are necessary.
41. Leszek M. Sokołowski
General relativity, gravitational energy and spin-two field
Int. J. Geom. Meth. Mod. Phys. , vol. 4, pp. 1-23 (2007).
(Lectures given at the 42 Karpacz Winter School of Theoretical Physics, Lądek Zdrój, Poland, 6-11 February 2006, "Current
Mathematical Topics in Gravitation and Cosmology"):
In my lectures I will deal with three seemingly unrelated problems: i) to what extent is general relativity exceptional among metric gravity theories? ii) is it possible to define gravitational energy density applying field-theory approach to gravity? and iii) can a consistent theory of a gravitationally interacting spin-two field be developed at all? The connecting link to them is the concept of a fundamental spin-2 field. A linear spin-2 field encounters insurmountable inconsistencies when coupled to gravity. After discussing the inconsistencies of any coupling of the linear spin-2 field to gravity, I exhibit the origin of the fact that a gauge invariant field has the variational metric stress tensor which is gauge dependent. I give a general theorem explaining under what conditions a symmetry of a field Lagrangian becomes also the symmetry of the stress tensor. It is a conclusion of the theorem that any attempt to define gravitational energy density in the framework of a field theory of gravity must fail. Finally I make a very brief introduction to basic concepts of how a certain kind of a necessarily nonlinear spin-2 field arises in a natural way from vacuum higher derivative gravity theories. This specific spin-2 field consistently interacts gravitationally.
42. Andrzej Woszczyna
Mechanika zaburzeń skalarnych w radiacyjnym wszechświecie
Prace Komisji Astrofizyki PAU, vol. 11, p. 117 (2007).