Quasilinear observables in dark energy cosmologies

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 $b_2$.