any dark energy model in particular. It is only then that we use these model-independent observables to construct tests which might eliminate or confirm particular models. Our approach is closest in spirit to Ref. [@Zhang:2007nk], the results of which we extend.

In this paper, we completely ignore the practical problems and limitations of the observations and assume that good-enough statistics with sufficiently small systematic errors can be achieved in the range of redshifts and scales discussed here. By exploring this idealized case we try to discover the fundamental limits to which observations in a dark energy cosmology are subject.

We adopt metric signature $(-+++)$, while a comma denotes a partial derivative. We interchangeably use coordinate time $t$, scale factor $a$, $e$-foldings $N\equiv\ln a$ and the redshift $z$ as time variables. Overdots denote derivatives with respect to $t$, primes with respect to $N$. The subscript $0$ denotes the present time. We also make use of the notation of [@DeFelice:2011bh; @DeFelice:2011hq], to which we refer for a thorough study of linear perturbations in the context of the Horndeski theories.

Assumptions {#sec:Assumpts}
===========

In keeping with the spirit of generality, we first wish to make the minimum of assumptions on the geometry and 