The Cosmic Causal Mass

In order to provide a better understanding of rotating universe models, and in particular the G\"{o}del universe, we discuss the relationship between cosmic rotation and perfect inertial dragging. In this connection, the concept of \emph{causal mass} is defined in a cosmological context, and discussed in relation to the cosmic inertial dragging effect. Then, we calculate the mass inside the particle horizon of the flat $\Lambda$CDM-model integrated along the past light cone. The calculation shows that the Schwarzschild radius of this mass is around three times the radius of the particle horizon. This indicates that there is close to perfect inertial dragging in our universe. Hence, the calculation provides an explanation for the observation that the swinging plane of a Foucault pendulum follows the stars.
Comment: 17 pages, 3 figures