Double-Kasner spacetime: Peculiar velocities and cosmic jets

Abstract

In dynamic spacetimes in which asymmetric gravitational collapse/expansion is taking place, the timelike geodesic equation appears to exhibit an interesting property: Relative to the collapsing configuration, free test particles undergo gravitational "acceleration" and form a double-jet configuration parallel to the axis of collapse.We illustrate this aspect of peculiar motion in simple spatially homogeneous cosmological models such as the Kasner spacetime. To estimate the effect of spatial inhomogeneities on cosmic jets, timelike geodesics in the Ricci-flat double-Kasner spacetime are studied in detail. While spatial inhomogeneities can significantly modify the structure of cosmic jets, we find that under favorable conditions the double-jet pattern can initially persist over a finite period of time for sufficiently small inhomogeneities.

Spontaneous dimensional reduction?

“…To connect this behavior to dimensional reduction, observe that while Kasner space is (3+1)-dimensional, it acts in important ways as if it were (1+1)-dimensional [2,3,39]. For example, consider a geodesic starting at a random point with a random initial direction.…”

Chaotic spin precession in anisotropic universes and fermionic dark matter

“…Moreover, due to equivalence principle, these conclusions may be extended to particles of any spin [20] and also to classical rotators [7]. The latter fact opens the possibility to study the role of the discussed precession effects for the formation of structures in the very early universes and angular momentum of cosmic strings [21]. Also, equivalence principle leads to the precession frequencies of spin and velocity differing by factor 2, so that the helicity is conserved in the non-inertial frame rotating with the same frequency but it is flipped [20] in the inertial frame.…”

Spin precession in anisotropic cosmologies

“…The spin dynamics in that case is manifesting the interesting effects [30]. Other interesting directions of investigation could be connected with the study of the spin precession in Bianchi II universes, in the generalized Melvin cosmologies in the presence of electromagnetic fields [31] and in the double Kasner universes [26]. We hope to study these topics in detail in future publications.…”

“…Moreover, due to the equivalence principle, these conclusions may be extended to particles of any spin [25] and also to classical rotators [11]. The latter fact opens the possibility to study the role of the discussed precession effects for the formation of structures in the very early universes and angular momentum of cosmic strings [26]. Also, the equivalence principle leads to the precession frequencies of spin and velocity differing by factor 2, so that the helicity is conserved in the non-inertial frame rotating with the same frequency but it is flipped [25] in the inertial frame.…”

“…Let us consider an opposite limiting case when the time parameter t is big enough to make the term C 1 /t p 1 dominating in the expression (26). (Let us note, however, that the value of the time parameter is still not as big to make the Kasner regime invalid and to have a transition to the isotropization due to the presence of matter, which will be described in the next section.)…”