Brane classical and quantum cosmology from an effective action

Abstract

Motivated by the Randall-Sundrum brane-world scenario, we discuss the classical and quantum dynamics of a (d + 1)-dimensional boundary wall between a pair of (d + 2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general -but not completely arbitrary -matter fields living on the boundary "brane universe" and its geometry is that of an FriedmannLemaître-Robertson-Walker (FLRW) model. The effective action governing the model in the minisuperspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semi-classical level; these correspond to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semi-classical level, and we consider the possible localization of the brane universe's wavefunction away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections.

FRW quantum cosmology with a generalized Chaplygin gas

“…This suggests a view that FRW models with a generalized Chaplygin gas content may enable us to investigate specific aspects within brane-worlds. E.g., the quantum cosmological creation of the universe, by means of an Hamiltonian formulation, taking into account the presence of potential symmetries and conserved charges that could be related with physical quantitites in brane-world physics [35,39,40,41,42,43,44,45].…”

“…Ref. [35,39,40,41,42,43,44,45]) can admit a phenomenological description in terms of a generalized Chaplygin gas minisuperspace cosmology. This could be investigated by means of suitable canonical transformations at the Hamiltonian formulation.…”

“…Interesting proposals, regarding the quantum cosmological creation of brane world models, were recently introduced and analysed in Ref. [35,39,40,41,42,43,44,45].…”

Universes encircling five-dimensional black holes

“…That is, in both the lmw and fsw coordinates, universes are defined simply as 4-surfaces comoving in ℓ or w. And unlike standard Schwarzschild-like coordinates, the lmw or fsw 5-metrics are regular as the universe crosses the black hole horizon(s). Such coordinates may have some utility in the study of quantized braneworld models, where the bad behaviour of coordinates across horizons apparently results in a complicated canonical phase-space description of the brane's dynamics 23 . Finally, we discuss the temptation to generalize these coordinates to other types of black holes and different dimensions.…”

Creation of Neutral Fundamental Particles in the Weyl–Dirac Version of Wesson’s IMT

“…The notations as well as the geometric construction given below accord to these given in works of Paul Wesson and Sanjeev S. Seahra (1,2,3,4,5) .…”