Munshi, D;
(2018)
Symmetries, invariants and generating functions: higher-order statistics of biased tracers.
Journal of Cosmology and Astroparticle Physics
, 2018
(Jan)
, Article 53. 10.1088/1475-7516/2018/01/053.
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Abstract
Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast δ_h with the underlying density contrast δ, divergence of velocity θ and their higher-order derivatives. This is done by constructing invariants such as s, t, ψ,η. We show how the generating function formalism in Eulerian standard perturbation theory (SPT) can be used to show that many of the additional terms based on extended Galilean and Lifshitz symmetry actually do not make any contribution to the higher-order statistics of biased tracers. Other terms can also be drastically simplified allowing us to write the vertices associated with δ_h in terms of the vertices of δ and θ, the higher-order derivatives and the bias coefficients. We also compute the cumulant correlators (CCs) for two different tracer populations. These perturbative results are valid for tree-level contributions but at an arbitrary order. We also take into account the stochastic nature bias in our analysis. Extending previous results of a local polynomial model of bias, we express the one-point cumulants Script SN and their two-point counterparts, the CCs i.e. Script C_pq, of biased tracers in terms of that of their underlying density contrast counterparts. As a by-product of our calculation we also discuss the results using approximations based on Lagrangian perturbation theory (LPT).
| Type: | Article |
|---|---|
| Title: | Symmetries, invariants and generating functions: higher-order statistics of biased tracers |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1475-7516/2018/01/053 |
| Publisher version: | https://doi.org/10.1088/1475-7516/2018/01/053 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | cosmological simulations, galaxy clustering, galaxy surveys |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Space and Climate Physics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10056198 |
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