  We consider one-loop corrections to the bispectrum and skewness of
cosmological density fluctuations induced by gravitational evolution. As has
been established by comparison with numerical simulations, tree-level
perturbation theory (PT) describes these quantities at the largest scales.
One-loop PT provides a tool to probe the transition to the non-linear regime on
smaller scales. In this work, we find that, as a function of spectral index n,
the one-loop bispectrum follows a pattern analogous to that of the one-loop
power spectrum, which shows a change in behavior at a critical index n_c =
-1.4, where non-linear corrections vanish. For the bispectrum, for n less than
n_c, one-loop corrections increase the configuration dependence of the leading
order contribution; for n greater than n_c, one-loop corrections tend to cancel
the configuration dependence of the tree-level bispectrum, in agreement with
known results from n=-1 numerical simulations. A similar situation is shown to
hold for the Zel'dovich approximation (ZA), where n_c = -1.75. Using
dimensional regularization, we obtain explicit analytic expressions for the
one-loop bispectrum for n=-2 initial power spectra, for both the exact dynamics
of gravitational instability and the ZA. We also compute the skewness factor,
including local averaging of the density field, for n=-2: S_3(R) = 4.02 + 3.83
sigma^2(R) for gaussian smoothing and S_3(R) = 3.86 + 3.18 sigma^2(R) for
top-hat smoothing, where sigma^2(R) is the variance of the density field
fluctuations smoothed over a window of radius R. Comparison with fully
non-linear numerical simulations implies that, for n < -1, one-loop PT can
extend our understanding of nonlinear clustering down to scales where the
transition to the stable clustering regime begins.

Astrophysics