Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
- Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8 (Canada)
- Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON M5S 3H8 (Canada)
On very large scales, density fluctuations in the Universe are small, suggesting a perturbative model for large-scale clustering of galaxies (or other dark matter tracers), in which the galaxy density is written as a Taylor series in the local mass density, δ, with the unknown coefficients in the series treated as free ''bias'' parameters. We extend this model to include dependence of the galaxy density on the local values of ∇{sub i}∇{sub j}φ and ∇{sub i}v{sub j}, where φ is the potential and v is the peculiar velocity. We show that only two new free parameters are needed to model the power spectrum and bispectrum up to 4th order in the initial density perturbations, once symmetry considerations and equivalences between possible terms are accounted for. One of the new parameters is a bias multiplying s{sub ij}s{sub ji}, where s{sub ij} = [∇{sub i}∇{sub j}∇{sup −2}−(1/3)δ{sup K}{sub ij}]δ. The other multiplies s{sub ij}t{sub ji}, where t{sub ij} = [∇{sub i}∇{sub j}∇{sup −2}−(1/3)δ{sup K}{sub ij}](θ−δ), with θ = −(a H dln D/dln a){sup −1}∇bold dotv. (There are other, observationally equivalent, ways to write the two terms, e.g., using θ−δ instead of s{sub ij}s{sub ji}.) We show how short-range (non-gravitational) non-locality can be included through a controlled series of higher derivative terms, starting with R{sup 2}∇{sup 2}δ, where R is the scale of non-locality (this term will be a small correction as long as k{sup 2}R{sup 2} is small, where k is the observed wavenumber). We suggest that there will be much more information in future huge redshift surveys in the range of scales where beyond-linear perturbation theory is both necessary and sufficient than in the fully linear regime.
- OSTI ID:
- 22273228
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2009, Issue 08; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
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