The Thermodynamics of a Gravitating Vacuum

Abstract

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 ∈vac that is constant over the cosmic evolution. In this paper here we show, however, that this assumption of constant vacuum energy density is unphysical, since it conflicts with the requirements of cosmic thermodynamics. We start from the total vacuum energy including the negatively valued gravitational binding energy and show that cosmic thermodynamics then requires that the cosmic vacuum energy density can only vary with cosmic scale R = R(t) according to ∈vac  ~ R-v with only two values of v being allowed, namely v1 = 2 and v2 = 5/2. We then discuss these two remaining solutions and find, when requiring a universe with a constant total energy, that the only allowed power index is v1 = 2. We discuss the consequences of this scaling of ∈vac and show the results for a cosmic scale evolution of a quasi-empty universe like the one that we are presently faced by.