The growth of the density fluctuations in the scale-invariant theory:
  one more challenge for dark matter
  The growth of the density fluctuations is considered to be an important
cosmological test. In the standard model, for a matter dominated universe, the
growth of the density perturbations evolves with redshift z like (1/{1+z))^s
with s=1. This is not fast enough to form galaxies and to account for the
observed present-day inhomogeneities. This problem is usually resolved by
assuming that at the recombination epoch the baryons settle down in the
potential well of the dark matter previously assembled during the radiation era
of the universe. This view is challenged in the present paper by using the
recently proposed model of a scale-invariant framework for cosmology that
enlarges the invariance group subtending the theory of the gravitation.
  From the continuity equation, the Euler and Poisson equations written in the
scale-invariant framework, the equation governing the growth of the density
fluctuations is obtained. Starting from \delta = 10^{-5} at a redshift around
1000, numerical solutions for various density background are obtained. The
growth of density fluctuations is much faster than in the standard EdS model.
The s values are in the range from 2.7 to 3.9 for \Omega_m between 0.30 and
0.02. This enables the density fluctuations to enter the nonlinear regime with
\delta > 1 long before the present time, typically at redshifts of about 10,
without requiring the presence of dark matter.
