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.
