An alternative to the LCDM model: the case of scale invariance
  The hypothesis is made that, at large scales where General Relativity may be
applied, the empty space is scale invariant. This establishes a relation
between the cosmological constant and the scale factor of the scale invariant
framework. This relation brings major simplifications in the scale invariant
equations for cosmology, which now contain a new term, depending on the
derivative of the scale factor, that opposes to gravity and produces an
accelerated expansion. The displacements due to the acceleration term make a
high contribution Omega_l to the energy-density of the Universe, satisfying an
equation of the form Omega_m+\Omega_k+Omega_l = 1. The models do not demand the
existence of unknown particles. There is a family of flat models with different
density parameters Omega_m < 1.
  Numerical integrations of the cosmological equations for different values of
the curvature and density parameter k and Omega_m are performed. The presence
of even tiny amounts of matter in the Universe tends to kill scale invariance.
The point is that for Omega_m = 0.3 the effect is not yet completely killed.
The models with non-zero density start explosively with first a braking phase
followed by a continuously accelerating expansion. Several observational
properties are examined, in particular the distances, the m--z diagram, the
Omega_m vs. lambda plot. Comparisons with observations are also performed for
the Hubble constant H_0 vs. Omega_m, for the expansion history in the plot
H(z)/(z+1) vs. redshift z and for the transition redshift from braking to
acceleration. These first dynamical tests are satisfied by the scale invariant
models, which thus deserve further studies.
