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 similar to 1), like the Sunyaev-Zel'dovich survey proposed by the South Pole Telescope or a red sequence photometric survey with VISTA or the Dark Energy Survey, could potentially constrain the sound horizon scale to an accuracy of similar to 2 per cent, in turn fixing the ratio of the pressure of the dark energy to its density (w) to better than similar to 10 per cent. Our approach does not require knowledge of the cluster mass, unlike those that depend upon the abundance of clusters.