Scale invariant cosmology II: model equations and properties

We want to establish the basic properties of a scale invariant cosmology, that also accounts for the hypothesis of scale invariance of the empty space at large scales. We write the basic analytical properties of the scale invariant cosmological models. The hypothesis of scale invariance of the empty space at large scale brings interesting simplifications in the scale invariant equations for cosmology. There is one new term, depending on the scale factor of the scale invariant cosmology, that opposes to gravity and favours an accelerated expansion. We first consider a zero-density model and find an accelerated expansion, going like t square. In models with matter present, the displacements due to the new term make a significant contribution Omega_l to the energy-density of the Universe, satisfying an equation of the form Omega_m + Omega_k + Omega_l = 1. Unlike the Friedman's models, there is a whole family of flat models (k=0) with different density parameters Omega_m smaller than 1. We examine the basic relations between the density and geometrical properties, as well as the conservation laws. The models containing matter have an inflexion point, with first a braking phase followed by an accelerated expansion phase. The scale invariant models have interesting properties and deserve further investigations.