Electrocardiogram of the Mixmaster Universe

The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index S, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except the time used to parametrize it. Its graph versus time with typical spikes in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such spike pair arising from a single circuit or “pulse” around the origin in the complex plane. These pulses in the speciality index seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role in the current investigations of inhomogeneous Mixmaster dynamics.