Static universe model existing due to the matter-dark energy coupling

The work investigates a static, isotropic, and almost homogeneous Universe containing a real scalar field modeling the dark energy (DE) (quintessence) interacting with pressureless matter. It is argued that the interaction between matter and the DE is essential for the very existence of the considered solution. Assuming the possibility that DE can be furnished by the Dilaton (a scalar field reflecting the condensation of string states with zero angular momentum), we fix the value of scalar field at the origin to the Planck scale. It became possible to fix the ratio of the amount of DE to matter energy, in the currently estimated value 0.70.3 and also the observed magnitude of the Hubble constant. The mass of the scalar field chosen for fixing the above ratio and Hubble effect strength, results to be of the order of 10(-29) cm(-1), a small value which seems to be compatible with the zero mass of the Dilaton in the lowest approximations.