Self-calibration techniques for analyzing cluster counts rely on using the abundance and the clustering amplitude of clusters to simultaneously constrain cosmological parameters and the relation between halo mass and its observable mass tracer. It was recently discovered that the clustering amplitude of halos depends not only on halo mass, but also on various secondary variables such as halo formation time and concentration; these dependences are collectively termed 'assembly bias'. Using a modified Fisher matrix formalism, we explore whether these secondary variables have a significant impact on studying the properties of dark energy with self calibration in current (SDSS) and near future (DES, SPT, and LSST) cluster surveys. We find that for an SDSS-like survey, secondary dependences of halo bias are insignificant given the expected large statistical uncertainties in dark energy parameters. For SPT- or DES-like survey volumes, we find that the dependence of halo bias on secondary variables is not a significant systematic provided the scatter in the observable-mass relation is 20% or lower, as expected for X-ray or SZ surveys. At higher scatter (e.g. values currently possible with optical surveys), significant systematic errors are possible, depending on how strongly the cluster observable correlates with the secondary variables at fixed mass. For an LSST-like survey volume, this systematic is likely to be important even for lower scatter values or for less correlated observables.
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