Scale invariant cosmology I: the vacuum and the cosmological constant

The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic and large scales where General Relativity may be applied, the empty space in the sense it is used in the Minkowski metric, is also scale invariant. It is shown that if this applies, the Einstein cosmological constant and the scale factor of the scale invariant framework are related by two differential equations.