Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance

Several dark energy experiments are available from a single large-area imaging survey and may be combined to improve cosmological parameter constraints and/or test inherent systematics. Two promising experiments are cosmic shear power spectra and counts of galaxy clusters. However, the two experiments probe the same cosmic mass density field in large-scale structure, therefore the combination may be less powerful than first thought. We investigate the cross-covariance between the cosmic shear power spectra and the cluster counts based on the halo model approach, where the cross-covariance arises from the three-point correlations of the underlying mass density field. Fully taking into account the cross-covariance, as well as non-Gaussian errors on the lensing power spectrum covariance, we find a significant cross-correlation between the lensing power spectrum signals at multipoles l ∼10 3 and the cluster counts containing halos with masses M ≳10 14 M ⊙ . Including the cross-covariance for the combined measurement degrades and in some cases improves the total signal-to-noise (S/N) ratios up to ∼±20% relative to when the two are independent. For cosmological parameter determination, the cross-covariance has a smaller effect as a result of working in a multi-dimensional parameter space, implying that the two observables can be considered independent to a good approximation. We also discuss the fact that cluster count experiments using lensing-selected mass peaks could be more complementary to cosmic shear tomography than mass-selected cluster counts of the corresponding mass threshold. Using lensing selected clusters with a realistic usable detection threshold (( S / N ) cluster ∼6 for a ground-based survey), the uncertainty on each dark energy parameter may be roughly halved by the combined experiments, relative to using the power spectra alone.