Homogeneous Sphere with Excited Vacuum Pressure, Applications in Extended Space Model and Cosmology

In the paper vacuum pressure is found from the space geometry around the local gravity system according to Sakharov’s idea of a "metrical elasticity" of space. It is assumed that energy equivalent to the gravitational defect of masses is spent on vacuum deformation. We determined the gravitational impact on the vacuum in the case of weakly gravitating static centrally symmetric distribution of matter using appropriate solution of Einstein’s equations. This impact is balanced by the vacuum pressure of the opposite sign. The equation of state includes the density of matter and the vacuum pressure. They correspond to the field equations for centrally symmetric distribution of matter. The photon motion in the resulting space-time is considered and the energy-momentum-mass vector corresponding to the D Extended Space Model (ESM) is found. We study abilities to apply the equation of state obtained to arbitrary We study abilities to apply the equation of state obtained to arbitrary gravitational systems and cosmology. The change in photon energy and momentum in Friedmann-Lemaitre-Robertson-Walker space-time is described using rotation angles in 5D. This cosmological model yields about half dark energy density not associated with cosmological constant with half dark energy density not associated with cosmologic deceleration parameter at present epoch.