Determination of the Linear Mass Power Spectrum From the Mass Function of Galaxy Clusters

We develop a new method to determine the linear mass power spectrum using the mass function of galaxy clusters. We obtain the rms mass fluctuation sigma (M) using the expression for the mass function in the Press & Schechter (1974), Sheth, Mo & Tormen (2001) and Jenkins et al. (2001) formalisms. We apply different techniques to recover the adimensional power spectrum Delta ^{2}(k) from sigma (M) namely the k_{eff} approximation, the singular value decomposition and the linear regularization method. The application of these techniques to the tCDM and LCDM GIF simulations shows a high efficiency in recovering the theoretical power spectrum over a wide range of scales. We compare our results with those derived from the power spectrum of the spatial distribution of the same sample of clusters in the simulations obtained by application of the classical Feldman, Kaiser & Peacock (1994), FKP, method. We find that the mass function based method presented here can provide a very accurate estimate of the linear power spectrum, particularly for low values of k. This estimate is comparable, or even better behaved, than the FKP solution. The principal advantage of our method is that it allows the determination of the linear mass power spectrum using the joint information of objects of a wide range of masses without dealing with specific assumptions on the bias relative to the underlying mass distribution.