We study the asymptotic behaviour of the free, cold-dark matter density
fluctuation bispectrum in the limit of small scales. From an initially Gaussian
random field, we draw phase-space positions of test particles which then
propagate along Zel’dovich trajectories. A suitable expansion of the initial
momentum auto-correlations of these particles leads to an asymptotic series
whose lower-order power-law exponents we calculate. The dominant contribution
has an exponent of $-11/2$. For triangle configurations with zero surface area,
this exponent is even enhanced to $-9/2$. These power laws can only be revealed
by a non-perturbative calculation with respect to the initial power spectrum.
They are valid for a general class of initial power spectra with a cut-off
function, required to enforce convergence of its moments. We then confirm our
analytic results numerically. Finalmente, we use this asymptotic behaviour to
investigate the shape dependence of the bispectrum in the small-scale limit,
and to show how different shapes grow over cosmic time. These confirm the usual
model of gravitational collapse within the Zel’dovich picture.

Questo articolo esplora i giri e le loro implicazioni.

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