It has been shown that in an idealized galaxy cluster survey , containing \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ > $ } 10 , 000 clusters , statistical errors on dark energy and other cosmological parameters will be at the percent level .
Furthermore , through “ self–calibration ” , parameters describing the mass–observable relation and cosmology can be simultaneously determined , though at a loss in accuracy by about an order of magnitude .
Here we examine an alternative approach to self–calibration , in which a parametrized ab–initio physical model is used to compute theoretical mass–observable relations from the cluster structure .
As an example , we use a modified–entropy ( “ preheating ” ) model of the intracluster medium , with the history and magnitude of entropy injection as unknown input parameters .
Using a Fisher matrix approach , we evaluate the expected simultaneous statistical errors on cosmological and cluster model parameters .
We find that compared to a phenomenological parametrization of the mass–observable relation , our physical model yields significantly tighter constraints in both surveys , and offers substantially improved synergy when the two surveys are combined .
In a mock X–ray survey , we find statistical errors on the dark energy equation of state are a factor of two tighter than the phenomenological model , with \Delta w _ { 0 } \sim 0.08 and its evolution , \Delta w _ { a } \equiv - \Delta dw / da \sim 0.23 , with corresponding errors of \Delta w _ { 0 } \sim 0.06 and \Delta w _ { a } \sim 0.17 from a mock Sunyaev-Zel ’ dovich ( SZ ) survey , both with N _ { cl } \sim 2.2 \times 10 ^ { 4 } clusters , while simultaneously constraining cluster model parameters to \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ < $ } 10 \% .
When the two surveys are combined , the constraints tighten to \Delta w _ { 0 } \sim 0.03 and \Delta w _ { a } \sim 0.1 ; a 40 % improvement over adding the individual experiment errors in quadrature , and a factor of 2 improvement over the phenomenological model .
This suggests that parametrized physical models of cluster structure will be useful when extracting cosmological constraints from SZ and X–ray cluster surveys .