On dynamical systems approaches and methods in f ( R ) cosmology
- Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
- Centro Multidisciplinar de Astrofisica – CENTRA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
- Department of Physics, Karlstad University, S-65188 Karlstad (Sweden)
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.
- OSTI ID:
- 22679482
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 08; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
Similar Records
Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory
Higher powers in gravitation