Highly Excited Friedmann Universe

A highly excited Friedmann universe filled with a scalar field and radiation has been considered. On the basis of a direct solution to the quantum-mechanical problem with a well-defined time variable, it has been shown that such a universe can have features (energy density, scale factor, Hubble constant, density parameter, matter mass, equivalent number of baryons, age, dimensions of large-scale fluctuations, amplitude of fluctuations of cosmic microwave background radiation temperature) identical to those of the currently observed Universe. 1. Available cosmological data suggest that, from the point of view of quantum theory , the currently observed Universe is likely to be in a highly excited state [1]. This is confirmed by estimates of the number of the quantum state that corresponds to its averaged motion as a discrete unit [1-4]. In view of this, it is important to investigate cos-mological systems featuring gravitational and matter fields and occurring in states with large quantum numbers by proceeding from a direct solution to the relevant quantum-mechanical problem. A model of the Friedmann universe filled with a uniform scalar field has been proposed in [4]. This model, which is appropriate for constructing a quantum theory, features a well-defined time variable. The reference frame was specified there with the aid of a subsidiary matter source in the form of radiation (relativistic matter of any nature) that was assumed to be initially present in the cosmological system along with a scalar field that forms a nonzero cosmological constant in the early universe. The evolution of the universe filled with not only scalar field but also with radiation differs from that which is realized in the absence of radiation. The main difference lies here in the emergence of a new region that is accessible to a classical motion and which is bounded by the potential barrier existing in the system of scalar and gravitational fields. A quantum universe involving a slowly varying scalar field and occurring in low-lying (quasistationary) states has been analyzed in [4], where it has been shown that the dynamical model proposed there is compatible with the currently prevailing ideas of the early Universe. In this study, we will consider a quantum Friedmann universe with large quantum numbers characterizing the possible physical states of the gravitational and matter fields involved. On the basis of a solution to the quantum mechanical problem, it is shown that the universe in highly excited states can have …