Vacuum fluctuations, isolated systems and hierarchical cosmology

Einstein's general theory of relativity rests on the convention of constant units for time and length, specified by standards at a fixed world point P. It is valid to flatten space-time by choice of unit fields, obtained by applying time dilation and length contraction to standards in accordance with an aether velocity field v
g
(r, t). Two equally valid descriptions for gravitation result. Cosmology in flat space-time is first developed. Zero-point radiation is renormalized to finite energy Kρ
0
c
²
density by inclusion of gravitational self-potential energy density provided that Kρ
0
c
²
closes the universe at radius R. It is shown that such a universe satisfies the black hole condition, and hence behaves as an isolated system. A single constant defines a finite universe with respect to any mass, due to self-adjustment of boundary surface. The equivalent Einstein model is found by a units transformation to be de Sitter space-time. Einstein's equations must contain only the cosmological term as source term. The Hubble redshift is shown to emerge in both Doppler-gravitational and frequency-decay guises. By postulating an infinite Cosmos containing universes on a hierarchy of scales specified by a geometric series of constants, it is possible for gravitation and electromagnetism to acquire equal complementary status. Unified field equations are proposed, and the relationship between an electron and a universe is explored. A theoretical value of the Hubble constant emerges, H = 108 km s
⁻¹
M pc
⁻¹
.