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Title: Non-linear stochastic growth rates and redshift space distortions

The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc-1 to 25 per cent at k ~ 0.45 h Mpc-1 at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 1012 M h-1, compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -fLTδ, where fLT is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc-1. Furthermore, the stochasticity in the θ – δ relation is not somore » simply described by 2LPT, and we discuss its impact on measurements of fLT from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of fLT extracted using models which assume a linear, deterministic expression.« less
 [1] ;  [2]
  1. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Univ. of Chicago, IL (United States)
  2. Imperial College London, London (United Kingdom)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1365-2966; arXiv eprint number arXiv:1502.02052
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Monthly Notices of the Royal Astronomical Society (Online)
Additional Journal Information:
Journal Name: Monthly Notices of the Royal Astronomical Society (Online); Journal Volume: 449; Journal Issue: 4; Journal ID: ISSN 1365-2966
Royal Astronomical Society
Research Org:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
79 ASTRONOMY AND ASTROPHYSICS methods: N-body simulations; cosmology: theory; large-scale structure of universe