  An accurate theoretical description of structure formation at least in the
mildly non-linear regime is essential for comparison with data from next
generation galaxy surveys. In a recent approach one follows the time evolution
of correlators directly and finds a hierarchy of evolution equations with
increasing order (Pietroni 2008). So far, in this so called time
renormalisation group method the trispectrum was neglected in order to obtain a
closed set of equations. In this work we study the influence of the trispectrum
on the evolution of the power spectrum. In order to keep the numerical cost at
a manageable level we use the tree-level trispectrum from Eulerian perturbation
theory. In comparison to numerical simulations we find improvement in the
mildly non-linear regime up to k = 0.25 h/Mpc. Beyond k = 0.25 h/Mpc the
perturbative description of the trispectrum fails and the method performs worse
than without the trispectrum included. Our results reinforce the conceptual
advantage of the time renormalisation group method with respect to perturbation
theory.
