  The gravitational evolution of scale free initial spectra $P(k)\propto k^n$
in an Einstein-de Sitter universe is widely believed to be self-similar for
$-3<n<4$. However, for $-3<n<-1$ the existence of self-similar scaling has not
been adequately demonstrated. Here we investigate the possible breaking of
self-similar scaling due to the nonlinear contributions of long wave modes. For
$n<-1$ the nonlinear terms in the Fourier space fluid equations contain terms
that diverge due to contributions from wavenumber $k\to 0$ (the long wave
limit). To assess the possible dynamical effects of this divergence the limit
of long wave contributions is investigated in detail using two different
analytical approaches.
  Perturbative contributions to the power spectrum are examined. It is shown
that for $n<-1$ there are divergent contributions at all orders. However, at
every order the leading order divergent terms cancel out exactly. This does not
rule out the existence of a weaker but nevertheless divergent net contribution.
The second approach consists of a non-perturbative approximation, developed to
study the nonlinear effects of long wave mode coupling. A solution for the
phase shift of the Fourier space density is obtained which is divergent for
$n<-1$. A kinematical interpretation of the divergence of the phase shift,
related to the translational motion induced by the large-scale bulk velocity,
is given. Our analysis indicates that the amplitude of the density is {\it not}
affected by the divergent terms. Thus both analytical approaches lead to the
conclusion that the self-similar scaling of physically relevant measures of the
growth of density perturbations is preserved.
