On the causality aspects of the dynamical Chern-Simons modified gravity

We discuss the G\"{o}del-type solutions within the dynamical Chern-Simons modified gravity in four dimensions. Within our study, we show that in the vacuum case the causal solutions are possible which cannot take place within the non-dynamical framework. Another our result consists in the possibility for completely causal solutions for all types of matters we study in the paper, that is, relativistic fluid, cosmological constant, scalar and electromagnetic fields.