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

According to Sakharov’s theory of the “metrical elasticity” of space, vacuum pressure in the paper is calculated from the geometry of the space around the local gravity system. Vacuum deformation is thought to consume energy equal to the gravitational defect of masses. Using an adequate solution of Einstein’s equations, we were able to estimate the gravitational influence on the vacuum in the situation of a weakly attracting static, centrally symmetric distribution of matter. The vacuum pressure of the opposing sign counteracts this effect. The vacuum pressure and matter density are both included in the equation of state. They match the field equations for the symmetric distribution of matter at the centre. The energy-momentum-mass vector corresponding to the D Extended Space Model (ESM) is discovered after taking into account the photon motion in the resultant space-time. We research the capacity to use the given equation of state for any We look at how well the derived equation of state may be applied to various gravitational systems and cosmology. Rotation angles in 5D are used to explain the change in photon energy and momentum in Friedmann-Lemaitre-Robertson-Walker space-time. This cosmological model predicts that during the current epoch, half of the dark energy density that is not linked with the cosmological constant and half of the dark energy density that is not related with the cosmic deceleration parameter.

**Author(s) Details:**

**D. Yu. Tsipenyuk,
**Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow, 119991 Russia and Moscow Politechnic University, Moscow, 107023 Russia.

**W. B. Belayev,
**Khlopin Radium Institute, Saint-Petersburg, 188651, Russia.

**Please see the link here:** **https://stm.bookpi.org/NTPSR-V6/article/view/7224**