  The cosmological fluid equations describe the early gravitational dynamics of
cold dark matter (CDM), exposed to a uniform component of dark energy, the
cosmological constant $\Lambda$. Perturbative predictions for the fluid
equations typically assume that the impact of $\Lambda$ on CDM can be
encapsulated by a refined growing mode $D$ of linear density fluctuations. Here
we solve, to arbitrary high perturbative orders, the nonlinear fluid equations
with an {\it Ansatz} for the fluid variables in increasing powers of $D$. We
show that $\Lambda$ begins to populate the solutions starting at the fifth
order in this strict $D$-expansion. By applying suitable resummation
techniques, we recast these solutions to a standard perturbative series where
not $D$, but essentially the initial gravitational potential serves as the
bookkeeping parameter within the expansion. Then, by using the refined growth
functions at second and third order in standard perturbation theory, we
determine the matter power spectrum to one-loop accuracy as well as the
leading-order contribution to the matter bispectrum. We find that employing our
refined growth functions impacts the total power- and bispectra at a precision
that is below one percent at late times. However, for the power spectrum, we
find a characteristic scale-dependent suppression that is fairly similar to
what is observed in massive neutrino cosmologies. Therefore, we recommend
employing our refined growth functions in order to reduce theoretical
uncertainties for analysing data in related pipelines.
