where n is the index of the power spectrum of the fluctuations in the early universe P ( k ) ∝ ∝ k n , ρ ρ ¯ ¯ is the mean (baryonic and dark) matter density of the universe at the time the fluctuation from which the object was formed had gravitationally collapsed, and M ∗ ∗ is a cut-off mass below which structures will form. Its value is: