Cosmic Vacuum Energy Determining the Space-Time Geometry of the Empty Universe

Different from energies constituted by baryons or photons both of which are expressed as energiesper particle, vacuum energy by its nature represents a ”volume energy”, i.e. an energy represented bythe sheer space volume, however, not simply reacting to the temporal change of this space volume,but rather in a non-evident way which we here try to fix using thermodynamic principles. Vacuumenergy is interpreted as a phenomenon of a polarization of empty space by real cosmic matter withthe consequence that the prevailing vacuum energy should depend on the cosmic matter density. Wetry to interpret vacuum energy as a form of a heat capacity of cosmic volumes and study by the use ofthermodynamical principles how the heat content of cosmic volumes should change with the changeof the volumes themselves. In the present days of modern cosmology, it is assumed that the mainingredient to cosmic energy presently is vacuum energy with an energy densityεvacthat is constantover the cosmic evolution. This paper shows that this assumption of constant vacuum energy densityis unphysical, since it conflicts with the requirements of cosmic thermodynamics. The study startsfrom the total vacuum energy including the negatively valued gravitational binding energy and showsthat cosmic thermodynamics then requires the cosmic vacuum energy density which can only varywith cosmic scaleR=R(t)according toεvacRwith only two values ofνbeing allowed, namelyν1= 2andν2= 5/2. The study then discusses these two remaining solutions and find, whenrequiring a universe with a constant total energy, that the only allowed power index isν1= 2. Theconsequences of this scaling ofεvacare discussed and the results for a cosmic scale evolution of aquasi-empty universe are presented.

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