Effective relational dynamics of a nonintegrable cosmological model

TL;DR

This paper investigates the relational dynamics of a nonintegrable cosmological model using an effective semiclassical approach, revealing conditions under which relational evolution is possible or breaks down due to classical trajectory defocusing.

Contribution

It applies the effective approach to a complex nonintegrable cosmological model, demonstrating how relational evolution can be analyzed with multiple clocks and identifying regions where it fails.

Findings

Relational evolution is feasible for sufficiently semiclassical states.

Relational evolution breaks down near maximal expansion due to trajectory defocusing.

States initially sharply peaked spread rapidly, causing mixing of internal time directions.

Abstract

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.