Intrinsic uncertainty on the nature of dark energy

We argue that there is an intrinsic noise on measurements of the equation of state parameter $w=p\mathrm{/}\rho$ from large-scale structure around us. The presence of the large-scale structure leads to an ambiguity in the definition of the background universe and thus there is a maximal precision with which we can determine the equation of state of dark energy. To study the uncertainty due to local structure, we model density perturbations stemming from a standard inflationary power spectrum by means of the exact Lema^{i}tre-Tolman-Bondi solution of Einstein’s equation, and show that the usual distribution of matter inhomogeneities in a $\mathrm{\Lambda }$CDM cosmology causes a variation of $w$ – as inferred from distance measures – of several percent. As we observe only one universe, or equivalently because of the cosmic variance, this uncertainty is systematic in nature.