  Maxwell equations and the equations of General Relativity are scale invariant
in empty space. The presence of charge or currents in electromagnetism or the
presence of matter in cosmology are preventing scale invariance. The question
arises on how much matter within the horizon is necessary to kill scale
invariance. The scale invariant field equation, first written by Dirac in 1973
and then revisited by Canuto et al. in 1977, provides the starting point to
address this question. The resulting cosmological models show that, as soon as
matter is present, the effects of scale invariance rapidly decline from \rho=0
to \rho_c and are forbidden for densities above \rho_c. The absence of scale
invariance in this case is consistent with considerations about causal
connection. Below \rho_c, scale invariance appears as an open possibility,
which also depends on the occurrence of inflation in the scale invariant
context. In the present approach, we identify the scalar field of the empty
space in the Scale Invariant Vacuum (SIV) context to the scalar field \phi in
the energy density expression of the vacuum at inflation. This leads to some
constraints on the potential. This identification also solves the so-called
``cosmological constant problem''. In the framework of scale invariance,an
inflation with a large number of e-foldings is also predicted. We conclude that
scale invariance for models with densities below \rho_c is an open possibility;
the final answer may come from high redshift observations, where differences
from the LCDM models appear.
