Effective relational dynamics of a nonintegrable cosmological model

We apply the effective approach to evaluating semiclassical relational dynamics to the closed Friedman-Robertson-Walker cosmological model filled with a minimally coupled massive scalar field. This model is interesting for studying relational dynamics in a more general setting because (i) it features a nontrivial coupling of the relational clock to the evolving degrees of freedom, (ii) no temporally global clock variable exists, and (iii) it is nonintegrable, which is typical for generic dynamical systems. The effective approach is especially well geared for addressing the concept of relational evolution in this context, since it enables one to switch between different clocks and yields a consistent (temporally) local time evolution with transient observables so long as semiclassicality holds. We provide evidence that relational evolution in this model universe, while possible for sufficiently semiclassical states, generically breaks down in the region of maximal expansion. This is rooted in a defocusing of classical trajectories, which leads to a rapid spreading of states that are initially sharply peaked and to a mixing of internal time directions in this region. These results are qualitatively compared to previous work on this model, revisiting conceptual issues that have been raised earlier in the literature.