Quantum Cosmology of the Quantum Space-Time.
Sergei Afanas'ev
Ioffe Physico-Technical Institute
serg@pl.school.ioffe.ru
Additional authors:
The idea of the quantum space-time appears as the development of the ideas of the quantum field theory, the metrical theory of the gravitation and the superstring theory representation about the nature of the particles as the extended objects excitations. The quantum space-time (QST) are represented as the set of the quantum states on the set of discretizations with the arbitrary form of the boundaries of the regions. There are some intellectual ways to this construction. Firstly, this concept of QST can be obtained by the analysis of the possibility of the realization of the concept of the space-time fundamental element as the quantum object. Because the space-time fundamental element is the quantum object, it cannot have the determined values of the geometrical variables (sizes, curvature etc.) and can be described by the distribution of the probability of the different values of its variables. Secondly, this concept can be obtained from the general theory of the mathematical structures deformation. With the consideration of the discrete structure of the space-time with the determined form (or the set of forms) of the fundamental element - the Regge space-time, the cubic lattice space-time etc., it can be noted that the deformation of the boundary of any determined form fundamental element leads to the idea of arbitrary form of the boundaries. The space-time with the arbitrary form of the fundamental element can be probabilistic one only, and the possible mathematical construction, described this random discrete space-time is the set of discretizations with the arbitrary form of regions boundaries with the distribution of the probability density on this set. Besides the represented two ways there are some ways to this construction. The set of the discretizations with the arbitrary form of the boundaries of regions have the some positive properties in comparison with the method of the definition of the random discrete space-time as the probabilistic space on the space-time topology. Firstly, this is the possibility of the structure of the metric space introduction. Obviously, the linear space of the quantum states is defined on the metric space naturally, then on the so set as the topology. Secondly, this is the potential possibility to defined the group of the transformations of the set of discretizations with the arbitrary form of the regions boundaries. These transformations are the motions of the boundaries of regions. It can be noted that the odd supersymmetry generators are the generators of the creation and destruction of the infinite small regions. The particles are represented as the excited states of the space of quantum states of QST. The different excited states differ one from other by the different values of the probabilistic characteristics of the fundamental elements - average values of the geometric variables of the fundamental elements, their correlation functions etc. It can be shown that the superstring theory principally is represented as the theory of two-dimensional localized basis in the space of the excited states of the quantum space-time in the limiting case when the length of the excitation on the space-like dimension is much greater then the fundamental length. The cosmological evolution description in the QST representation is based on the representations of cosmological (space-time) vacuum and the excited states of the all space-time (the Universe). The cosmological vacuum in this theory is the states with uniform-distributed the space-time fundamental elements geometrical values, including the values of the dimensionality of the space-time and the values of the average linear size of fundamental elements - the fundamental length. The cosmological evolution is possible in the one of the excited state of the quantum space-time. The excited states have the determined average values of some cosmological "parameters" : the dimensionality of the space-time, the gauge group, the values of the spontaneously breaking of the symmetries (supersymmetry, gauge symmetry, CPT-, C-, P-, CP- symmetries etc.). The inflation stage is the one with the strong probability of tunneling between the different excited states. It is the questions : there are the "localized" states (with the collapse in finish of cosmological evolution) only or have the time-infinite excited states the non-zero probability? The question : "What was before the zeroth time moment?" is absent in this description. The answers : 1) "One of the different "localized" excited states (with the different value of the average space-time dimensionality, the different gauge group etc.)" or 2) "Nothing" are identical in this description and have equal correctnesses.
