Modern Physics Letters A

Solutions of matrix quantum mechanics have been shown to describe time dependent backgrounds in the holographically dual two-dimensional closed string theory. We review some recent work dealing with nontrivial spacetimes which arise in this fashion and discuss aspects of physical phenomena in them. These include spacetimes with spacelike boundaries.

The noncommutative extension of two-dimensional BF model is considered. It is shown that the realization of the noncommutative map via the Groenewold–Moyal star product leads to instabilities of the action, hence to a non-renormalizable theory.

We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant Λ. The role of viscous fluid and Λ term in the evolution the BI spacetime is studied. Though the viscosity cannot remove the cosmological singularity, it plays a crucial part in the formation of a qualitatively new behavior of the solutions near singularity. It is shown that the introduction of the Λ term can be handy in the elimination of the cosmological singularity. In particular, in case of a bulk viscosity, a negative Λ provides a never-ending process of evolution, whereas, for some positive values of Λ and the bulk viscosity being inverse proportional to the expansion, the BI Universe admits a singularity-free oscillatory mode of expansion. In case of a constant bulk viscosity and share viscosity being proportional to expansion, the model allows both non-periodic and inflationary expansion independent to the sign of Λ term.

Propagation of fermions in curved spacetime generates gravitational interaction due to coupling of its spin with spacetime curvature connection. This gravitational interaction, which is an axial-four-vector multiplied by a four-gravitational vector potential, appears as a CPT violating term in the Lagrangian which generates an opposite sign and thus an asymmetry between the left-handed and the right-handed partners under the CPT transformation. In the case of neutrinos, this property can generate neutrino asymmetry in the Universe. If the background metric is of the rotating black hole, i.e. the Kerr geometry, this interaction for the neutrino is nonzero. Therefore the dispersion energy relation for the neutrino and its anti-neutrino are different which gives rise to the difference in their number densities and neutrino asymmetry in the Universe in addition to the known relic asymmetry.

Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are discussed. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of Ashtekar formalism in eight dimensions.

The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Schrödinger equation from noncommutative space to commutative space is obtained.

Considering the Møller energy definition in both Einstein's theory of general relativity and tele-parallel theory of gravity, we find the energy of the universe based on viscous Kasner-type metrics. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories and this result agrees with previous works of Cooperstock and Israelit et al., Banerjee–Sen, Vargas who investigated the problem of the energy in Friedmann–Robertson–Walker universe in Einstein's theory of general relativity and Aydogdu–Saltı who considered the same problem in tele-parallel gravity. In all of these works, they found that the energy of the Friedmann–Robertson–Walker spacetime is zero. Our result is the same as that obtained in the studies of Saltı and Havare. They used the viscous Kasner-type metric and found the total energy and momentum by using Bergmann–Thomson energy–momentum formulation in both general relativity and tele-parallel gravity. The result that the total energy and momentum components of the universe is zero supports the viewpoints of Albrow and Tryon.