Dynamical systems approaches and methods in cosmology

          @misc{ scivideos_PIRSA:17050054,
            doi = {10.48660/17050054},
            url = {https://pirsa.org/17050054},
            author = {Uggla, Claes},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Dynamical systems approaches and methods in cosmology},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2017},
            month = {may},
            note = {PIRSA:17050054 see, \url{https://scivideos.org/index.php/pirsa/17050054}}
          }
          

Abstract

I will with simple examples from spatially homogeneous and isotropic cosmology illustrate the importance of respecting the global features of a state space for a given model when reformulating field equations to useful dynamical systems. In particular I will use examples from f(R) gravity and GR with a minimally coupled scalar field. In this context I will also illustrate how various dynamical systems methods, such as, e.g., monotonic functions, center manifold techniques, averaging methods, can yield a global understanding of the solution spaces as well as approximations, complementing, e.g., the slow-roll approximation.