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 energies
per particle, vacuum energy by its nature represents a ”volume energy”, i.e. an energy represented by
the 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. Vacuum
energy is interpreted as a phenomenon of a polarization of empty space by real cosmic matter with
the consequence that the prevailing vacuum energy should depend on the cosmic matter density. We
try to interpret vacuum energy as a form of a heat capacity of cosmic volumes and study by the use of
thermodynamical principles how the heat content of cosmic volumes should change with the change
of the volumes themselves. In the present days of modern cosmology, it is assumed that the main
ingredient to cosmic energy presently is vacuum energy with an energy density ϵvac that is constant
over the cosmic evolution. This paper shows that this assumption of constant vacuum energy density
is unphysical, since it conflicts with the requirements of cosmic thermodynamics. The study starts
from the total vacuum energy including the negatively valued gravitational binding energy and shows
that cosmic thermodynamics then requires the cosmic vacuum energy density which can only vary
with cosmic scale R = R(t) according to ϵvac ∼ R
with only two values of ν being allowed, namely
ν1 = 2 and ν2 = 5/2. The study then discusses these two remaining solutions and find, when
requiring a universe with a constant total energy, that the only allowed power index is ν1 = 2. The
consequences of this scaling of ϵvac are discussed and the results for a cosmic scale evolution of a
quasi-empty universe are presented.