the HL [@Kimura:2011qn].\

Conclusions
===========

We have shown that cosmological linear observations can measure only $\Omega_{k0}$, $E\equiv H/H_{0}$ and the combinations $P_{1}=f/b$, $P_{2}=\Omega_{\text{m}0}\Sigma/f$ and $P_{3}=f+f'/f$. Parameters such as $\Omega_{\text{m}0}$, $\sigma_{8}$ or functions such as $Gf\sigma_{8}$ are not directly model-independent measurable quantities via linear cosmological observations alone. This limits in a fundamental way the knowledge of, among others, the evolution of the DE density parameter $\Omega_{x}$, its equation of state, or the matter growth rate $f$. From $E,P_{2,3}$ one can form consistency relations in terms of the HL functions. The simplest one is Eq.  or , expressed purely in terms of model-independent observables. If observations indicate a violation of a consistency relation, then the DE is not described by the HL in the quasi-static limit. Conversely, finding the predicted $k$-behavior would be a major confirmation of the scalar field picture of dark energy.

Non-linear effects will bring both more information and more unknowns into the picture so it is not clear how much, if at all, they would improve the task of reconstructing or rejecting the HL. The limitations of real-world observations, completely neglected here, are of course in practice the major hurdle on the path to this goal.

It is 