Context :

Aims : 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 .

Methods : We write the basic analytical properties of the scale invariant cosmological models .

Results : 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 favors an accelerated expansion .
We first consider a zero-density model and find an accelerated expansion , going like R ( t ) \sim t ^ { 2 } .
In models with matter present , the displacements due to the new term make a significant contribution \Omega _ { \lambda } to the energy-density of the Universe , satisfying an equation of the form \Omega _ { \mathrm { m } } + \Omega _ { \mathrm { k } } + \Omega _ { \lambda } = 1 .

Unlike the Friedman ’ s models , there is a whole family of flat models ( k = 0 ) with different density parameters \Omega _ { \mathrm { m } } < 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 .

Conclusions : The scale invariant models have interesting properties and deserve further investigations