Abstract
Making use of the
1
+
3
covariant formalism, we show explicitly the effect that nonmetricity has on the dynamics of the Universe. Then, using the Dynamical System Approach, we analyze the ...evolution of Bianchi type-I cosmologies within the framework of
gravity. We consider several models of function
, each of them manifesting isotropic eras of the Universe, whether transitional or not. In one case, in addition to the qualitative analysis provided by the dynamical system method, we also obtain analytical solutions in terms of the average length scale
l
.
We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability-induced renormalization triggered by the low-energy quantum fluctuations in a ...Universe with a positive cosmological constant. We use the dynamical systems approach to study the qualitative behavior of the Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize 'two regimes' dark energy phases, where an unstable early phase of power-law evolution of the scale factor is followed by an accelerated expansion era at late times.
We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in f ( R )-gravity. We argue that a complete description of the solution space of a model requires a global ...state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, f ( R ) = R + α R {sup 2}, α > 0, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to f ( R ) cosmology and discuss their advantages and disadvantages.
Junction conditions are discussed within the framework of f(R)-gravity with torsion. After deriving general junction conditions, the cases of coupling to a Dirac field and a spin fluid are explicitly ...dealt with. The main differences with respect to Einstein-Cartan-Sciama-Kibble theory (f(R)=R) are outlined.
We propose a new class of gravity theories which are characterized by a nontrivial coupling between the gravitational metric and matter mediated by an auxiliary rank-2 tensor. The actions generating ...the field equations are constructed so that these theories are equivalent to general relativity in a vacuum, and only differ from general relativity theory within a matter distribution. We analyze in detail one of the simplest realizations of these generalized coupling theories. We show that in this case the propagation speed of gravitational radiation in matter is different from its value in vacuum and that this can be used to weakly constrain the (single) additional parameter of the theory. An analysis of the evolution of homogeneous and isotropic spacetimes in the same framework shows that there exist cosmic histories with both an inflationary phase and a dark era characterized by a different expansion rate.
PDF
