  What are the fundamental limitations of reconstructing the properties of dark
energy, given cosmological observations in the quasilinear regime in a range of
redshifts, to be as precise as required? The aim of this paper is to address
this question by constructing model-independent observables, whilst completely
ignoring practical problems of real-world observations. Non-Gaussianities
already present in the initial conditions are not directly accessible from
observations, because of a perfect degeneracy with the non-Gaussianities
arising from the nonlinear matter evolution in generalized dark energy models.
By imposing a specific set of evolution equations that should cover a range of
dark energy cosmologies, we however find a constraint equation for the linear
structure growth rate $f_1$ expressed in terms of model-independent
observables. Entire classes of dark energy models which do not satisfy this
constraint equation could be ruled out, and for models satisfying it we could
reconstruct e.g. the nonlocal bias parameters $b_1$ and $b_2$.
