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Taka Matsubara (Nagoya Univ.)

35min. Nonlinear Perturbation Theory with Halo Bias and Redshift -space Distortions via the Lagrangian Picture. Taka Matsubara (Nagoya Univ.). “The Third KIAS Workshop on COSMOLOGY AND STRUCTURE FORMATION” Oct. 27 – 28, 2008, KIAS, Seoul 10/28/2008.

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Taka Matsubara (Nagoya Univ.)

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  1. 35min Nonlinear Perturbation Theory with Halo Bias and Redshift-space Distortions via the Lagrangian Picture Taka Matsubara (Nagoya Univ.) “The Third KIAS Workshop on COSMOLOGY ANDSTRUCTURE FORMATION” Oct. 27 – 28, 2008, KIAS, Seoul 10/28/2008

  2. Precision cosmology with galaxy clustering • BAO as a probe of dark energy In correlation function In power spectrum Eisenstein et al. (SDSS, 2005) Percival et al. (SDSS, 2007) DE is constrained by 1D scale: (SDSS survey)

  3. Theoretical modeling • The BAO dynamics is qualitatively captured by linear theory, but... • Nonlinearity in various aspects should be theoretically elucidated, otherwise the estimation of dark energy would be biased. • Nonlinearity in dynamics • Nonlinearity in redshift-space distortions • Nonlinearity in halo/galaxy bias

  4. Nonlinearity in dynamics • Nonlinear dynamics distorts the BAO signature • N-bodyexperiments • Simple nonlinear perturbation theory does not work well at relevant redshift z < 3 Correlation function, large N-body simulation Eisenstein et al. (2007) Power spectrum, large N-body simulation Seo et al. (2008) Power spectrum, N-body & 1-loop PT Meiksin et al. (1999)

  5. Nonlinearity in redshift-space distortions • Redshift-space distortions change the nonlinear effects on BAO • P(k): Small-scale enhancement relative to the large-scalepower is much less (but overall Kaiser enhancement) • x(r): Nonlinear degradation is larger N-body, Seo et al. (2005) N-body, Eisenstein et al. (2007)

  6. Nonlinearity in bias • Effects of nonlinear (halo) bias • P(k): Scale-dependent bias is induced by nonlinearity • x(r): Linear bias seems good for r > 60 h-1Mpc N-body, Angulo et al. (2005) N-body, Sanchez et al. (2008)

  7. Theories for nonlinear dynamics • Recent developments: nonlinearity in dynamics • Renormalized perturbation theory and its variants • Infinitely higher-order perturbations are reorganized and partially resummed “Renormalization group method” Matarrese & Pietroni (2008) “Closure theory” Taruya & Hiramatsu (2008) “Renormalized perturbation theory” Crocce & Scoccimarro (2008)

  8. Theory for nonlinear halo bias • Nonlinear perturbation theory with simple local bias is not straightforward • Smith et al. (2007): 1-loop PT + halo-like bias • McDonald (2006): bias renormalization } both in real space Smith et al. (2007) Jeong & Komatsu (2008)

  9. Nonlinear redshift distortions and bias • Redshift distortions & bias • Standard Eulerianperturbation theory + local bias model do not give satisfactory results… • Lagrangian picture is useful for these issues !! ： initial position : displacement vector : final position

  10. Redshift distortions in the Lagrangian picture • Redshift-space mapping is exactly “linear” even in the nonlinear regime • c.f.) In the Eulerian picture, the mapping is fully nonlinear: vz/(aH) x s z : line of sight

  11. 1-halo term 2-halo term The halo bias in the Lagrangian picture • Halo bias • (extended) Press-Schechter theory • Halo number density is biased in Lagrangian space • Lagrangian picture is natural for the halo bias • No need for assuming the spherical collapse model as in the usual halo approach

  12. Perturbation theory via the Lagrangian picture • Nonlinear dynamics + nonlinear halo bias + nonlinear redshift-space distortions (T.M. 2008) • Relation between the power spectrum and the displacement field Fourier transf. & Ensemble average Evaluation by adopting Lagrangianperturbation theory

  13. Diagrammatic representations are useful • Feynman rules • Relevant diagrams up to one-loop PT

  14. Result: nonlinear redshift-space distortions • Comparison of the one-loop PT to a N-body simulation Linear theory N-body 1-loop SPT This work This work N-body Linear theory (Points from N-body simulation of Eisenstein & Seo 2005)

  15. Result: halo bias in redshift space • The one-loop perturbation theory via the Lagrangian picture • Nonlinear dynamics + nonlinear halo bias + nonlinear redshift-space distortions P(k) x(r)

  16. Discussion • Galaxy bias • On large scales, halo bias ~ galaxy bias (2-halo term) • On small scales, 1-halo term should be included • 1-halo term in redshift space (White 2001; Seljak 2001;…) • Determination of the BAOscale • Scale dependence of the nonlinear halo bias • Smooth function, no characteristic scale • Shift of the BAO scale is correctable • P(k) vsx(r) • Not equivalent in data analysis with finite procedures

  17. Conclusions • Nonlinear modeling of the galaxy clustering is crucial for precision cosmology • Three main sources of nonlinear effects on LSS • Nonlinearity in dynamics • Nonlinearity in redshift-space distortions • Nonlinearity in halo/galaxy bias • Lagrangian picture is useful to elucidate above nonlinear effects (with perturbation theory)

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