Constraints on the dark energy equation of state from the imprint of baryons on the power spectrum of clusters

Acoustic oscillations in the baryon-photon fluid leave a signature in the matter power spectrum. The overall shape of the spectrum and the wavelength of the oscillations depend upon the sound horizon scale at recombination. Using the $\Lambda$ cold dark matter Hubble Volume simulation, we show that the imprint of baryons is visible in the power spectrum of cluster-mass dark matter haloes, in spite of significant differences between the halo power spectrum and the prediction of linear perturbation theory. A measurement of the sound horizon scale can constrain the dark energy equation of state. We show that a survey of clusters at intermediate redshift ($ z\sim1 $), like the Sunyaev-Zeldovich survey proposed by the South Pole Telescope or a red sequence photometric survey with VISTA, could potentially constrain the sound horizon scale to an accuracy of $\sim 2%$, in turn fixing the ratio of the pressure of the dark energy to its density ($w$) to better than $\sim 10%$. Our approach does not require knowledge of the cluster mass, unlike those that depend upon the abundance of clusters.