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The growth of the density fluctuations is considered to be an importantcosmological test. In the standard model, for a matter dominated universe, thegrowth of the density perturbations evolves with redshift z like (1/{1+z))^swith s=1. This is not fast enough to form galaxies and to account for theobserved present-day inhomogeneities. This problem is usually resolved byassuming that at the recombination epoch the baryons settle down in thepotential well of the dark matter previously assembled during the radiation eraof the universe. This view is challenged in the present paper by using therecently proposed model of a scale-invariant framework for cosmology thatenlarges the invariance group subtending the theory of the gravitation.  From the continuity equation, the Euler and Poisson equations written in thescale-invariant framework, the equation governing the growth of the densityfluctuations is obtained. Starting from \delta = 10^{-5} at a redshift around1000, numerical solutions for various density background are obtained. Thegrowth 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 and0.02. 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.

The growth of the density fluctuations in the scale-invariant theory: one more challenge for dark matter