1 / 11

A Closure Theory for Non-linear Evolution of Power Spectrum

2007/10/26 ROE-JSPS workshop 2007. arXiv:0708.1367 [astro-ph]. A Closure Theory for Non-linear Evolution of Power Spectrum. Atsushi Taruya ( RESCEU, Univ.Tokyo ). In collaboration with. Takashi Hiramatsu ( RESCEU, Univ.Tokyo ). Introduction and motivation.

emile
Télécharger la présentation

A Closure Theory for Non-linear Evolution of Power Spectrum

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 2007/10/26 ROE-JSPS workshop 2007 arXiv:0708.1367 [astro-ph] A Closure Theory for Non-linear Evolution of Power Spectrum Atsushi Taruya (RESCEU, Univ.Tokyo) In collaboration with Takashi Hiramatsu (RESCEU, Univ.Tokyo)

  2. Introduction and motivation Key ingredient in cosmology with galaxy redshift surveys: Baryon Acoustic Oscillations (BAOs) as cosmic standard ruler Constraining dark energy EOS: Seo & Eisenstein (2005) Rule-of-thumb Needs accurate theoretical predictions at least ~1% accuracy on P(k) or x(r) Among several systematic effects on P(k), “non-linear gravitational growth” we here consider

  3. 「New approach」 Based on field-theoretical approach, Standard PT calculation can be improved by re-summing an infinite class of perturbative corrections at all order. “Renormalized Perturbation Theory (RPT)” Crocce & Scoccimarro (2006ab,2007) Related works: McDonald, Matarrese & Pietroni, Valageas, Matsubara (‘07) Theoretical approach to non-linear gravitational growth Perturbation theory (PT) Perturbative treatment of (CDM+baryon) fluid system (analytic) (e.g., Suto & Sasaki 1991) Parameterized function calibrated by N-body simulation Fitting formulae (semi-analytic) (e.g., Peacock & Dodds 1996; Smith et al. 2003) N-body simulation Particle-based simulations treating (CDM + baryon) as self-gravitating N-body system (Numerical)

  4. z=0 One-loop PT Renormalized perturbation theory • Several approximations in practical use of RPT RPT • Reliability of N-body simulations (still few %) In this talk, Alternative approximate treatment is proposed based on the idea of RPT Linear Fitting formula RPT: demonstration Amongst various theoretical predictions, RPT reproduces the non-linear behaviors of BAOs in N-body simulations quite well. Crocce & Scoccimarro (2007)

  5. Basic Quantities in RPT • Non-linear Power spectrum • Non-linear propagator • Non-linear vertex function (a,b,c=1,2)

  6. Needs some approximations These are non-perturbative expressions in a sense that we need fully nonlinear theory for propagatorand vertex functionas well as power spectrum to predict something Renormalized Expressions linear P(k) Power spectrum Self-energy Linear propagator Self-energy Propagator

  7. linear P(k) Power spectrum self-energy Crocce & Scoccimarro (2007) Vertex function: Lowest-order evaluation (tree approx.) Self-energy: Born approximation replace with Propagator: Approximately including full-order non-linearity Corrections up to two-loop order are essential to reproduce the N-body results

  8. Closure Approximation AT & Hiramatsu, arXiv:0708.1367 Alternative self-consistent treatment to compute both non-linear power spectrum and propagator Lowest-order evaluation of vertex Truncation of higher-loop corrections than two-loop

  9. subscripts 1, 2 indicate = Time variable Closure Equations Evolution equations corresponding to the truncated diagrams: • Operator: • Fourier kernel:

  10. Results based on the Born approximation of self-energy up to one-loop order ) (i.e., replacing with Analytic results: P(k) and x(r) z=1 z=1 Standard PT (1-loop) Closure RPT Linear RPT Closure Linear N-body data: Jeong & Komatsu (2006)

  11. Summary Non-linear evolution of BAOs based on closure theory known as efficient treatment in subject of turbulence and non-equilibrium statistics “mode-coupling theory” “direct-interaction approximation” (e.g., Kraichnan 1959; Kawasaki 1970) Derivation of closure equations (Gaussian initial conditions) P(k) and x(r) Analytic treatment ※ Extention to non-Gaussian initial conditions is also possible For quantitative predictions for P(k) at k>0.2h/Mpc (z<1), full numerical treatment of closure equations is necessary Hiramatsu & AT (2007), in progress

More Related