Pengjie Zhang, Jun Pan, Yi Zheng
Massive spectroscopic surveys will open a new era of precision redshift space distortion (RSD) cosmology. We develop a new method to improve the RSD modeling and to carry out robust reconstruction of the 3D peculiar velocity through spectroscopic redshift surveys. (1) We propose a mathematically unique and physically motivated decomposition of peculiar velocity into three eigen-components. The three components have different origins, different scale dependences and different impacts on RSD. (2) This decomposition has the potential to simplify and improve the RSD modeling. We derive a new formula for the redshift space power spectrum. Under the velocity decomposition scheme, all high order Gaussian corrections and non-Gaussian correction of order $\delta^3$ can be taken into account without introducing extra model uncertainties. We also identify a significant systematical error causing underestimation of the structure growth parameter f by as much as $O(10%)$ even at relatively large scale k=0.1h/Mpc. (3) The velocity decomposition clarifies issues in peculiar velocity reconstruction through 3D galaxy distribution. We discuss two possible ways to fulfill the 3D velocity reconstruction. Both use the otherwise troublesome RSD in velocity reconstruction as a valuable source of information. Both have the advantage to render the reconstruction of a stochastic 3D field into the reconstruction of a deterministic window function W^s of limited degrees of freedom. Both can automatically and significantly alleviate the galaxy bias problem and, in the limit of a deterministic galaxy bias, completely overcome it. Paper I of this series of works lays out the methodology. Companion papers will extensively evaluate its performance against N-body simulations. [abridged]
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http://arxiv.org/abs/1207.2722
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