A noncommutative Friedman cosmological model

Abstract

The closed Friedman cosmological model, based on noncommutative geometry, is presented. Two global effects exhibited by the model are discussed. The first effect is the "generation of matter out of geometry". Gravitational field equation in this model has the form of the eigenvalue equation for the Einstein operator. It turns out that the eigenvalues of this operator reproduce components of the energy-momentum tensor. The second effect concerns the existence of the initial and final singularities. Because of the strongly probabilistic character of the noncommutative dynamics on the fundamental level, although singularities do exist, they are probabilistically irrelevant.

Fundamental Problems in the Unification of Physics

“…As we have seen above, the quantum sector of our model is essentially given by an algebra of random operators. In [11,23] we have demonstrated that the random character of the noncommutative regime makes singularities (even the strongest ones) probabilistically irrelevant. Computations for the closed Friedman world model [22] confirm that the modular evolution in this model goes through singularities without noticing them.…”

“…Mathematical aspects of the model were dealt with in [21], and its physical content in [22]. Details of the Friedman cosmological model were computed in [11,24]. Further works, especially regarding field theoretical and observational aspects of the model, are in progress.…”

Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

“…space, the states for a charged particle moving in a magnetic field should be described by the common Eigenvalues of this operator are integers and do not appear in the energy spectrum (21), which means the degenerate degree of the states is infinite. Up to now, the energy spectrum and quantum states for a charged particle moving in a magnetic field in 3D noncommutative phase space are derived.…”

“…Renewed interest in such an idea is mainly due to the recent discoveries in string theory and M theory that effects of noncommutative (NC) spaces may appear near the string scale and at higher energies [2][3][4]. Recently, a lot of investigations have been done on the theory of NC spaces [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] such as the quantum Hall effects (QHE) [7][8][9][10], the harmonic oscillator [11][12][13][14], the coherent states [15], the thermodynamics [16], the classical-quantum transition [17], etc.. The QHE [7][8][9][10] refers to the phenomenon that when a magnetic field perpendicular to the electric current flowing through an electric conductor is applied, there appears the potential difference (Hall voltage) in the direction perpendicular to the current and the magnetic field.…”