We describe a new method of overcoming problems inherent in peculiar velocity surveys by using data compression as a filter with which to separate large–scale, linear flows from small– scale noise that biases the results systematically. We demonstrate the effectiveness of our method using realistic catalogs of galaxy velocities drawn from N–body simulations. Our tests show that a likelihood analysis of simulated catalogs that uses all of the information contained in the peculiar velocities results in a bias in the estimation of the power spectrum shape parameter Γ and amplitude β, and that our method of analysis effectively removes this bias. We expect that this new method will cause peculiar velocity surveys to re–emerge as a useful tool to determine cosmological parameters. We introduce a new method for the analysis of peculiar velocity surveys 1,2 that is a significant improvement over previous methods. In particular, our formalism allows us to separate information about large–scale flows from information about small scales, the latter can then be discarded in the analysis. By applying specific criteria, we are able to retain the maximum information about large scales needed to place the strongest constraints, while removing the bias that small–scale information can introduce into the results. To analyze the observed line–of–sight velocities we assume that N objects with positions ri and observed line–of–sight velocities vi can be modeled as vi = v(ri) · ˆri + δi (1) where v(ri) is the linear velocity field and δi is the noise which also accounts for the deviations from linear theory. Assume the noise is Gaussian with variance σ 2 i + σ2 ∗ where σi is the observational error and σ ∗ is the contribution from nonlinearity and other things we neglected (see 3 for detail analysis). The covariance matrix can be written as Rij = 〈vi vj 〉 = R (v) ij + δij σ 2 i + σ 2) ∗ where R (v) ij = 〈v(ri) · ˆri v(rj) · ˆrj 〉. (2) In linear theory we can express the velocity power spectrum in terms of the density power spectrum and thus rewrite the above a
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