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. 
R. Angulo (1), C.M. Baugh (2), C.S. Frenk (2), R.G. Bower (2), A.   Jenkins (2), S.L. Morris (2) (1- Catolica, 2-Durham)