GENERAL RELATIVISTIC DESCRIPTION OF OBSERVED GALAXY POWER SPECTRUM

Transcription

1 GENERAL RELATIVISTIC DESCRIPTION OF OBSERVED GALAXY POWER SPECTRUM JAIYUL YOO INSTITUTE for THEORETICAL PHYSICS, UNIVERSITY of ZÜRICH Michigan Center for Theoretical Physics, May, 14,

2 CONTENTS I. Why? II. How? III. So What? 2

3 I. MOTIVATION theoretical inconsistency in the standard method is Newtonian description valid? larger volume and higher redshift primordial non-gaussianity on large scales it is general relativity! 3

4 GR Effects on Horizon which gauge choice?(there are infinitely many gauges) order one effects on horizon scale! Pm : Synchronous gauge, Pm : Newtonian gauge 4

5 GR Effects on Horizon which gauge choice?(there are infinitely many gauges) order one effects on horizon scale! Pm : Synchronous gauge, Pm : Newtonian gauge 4

6 GR Effects on Horizon which gauge choice?(there are infinitely many gauges) order one effects on horizon scale! Pm : Synchronous gauge, Pm : Newtonian gauge 4

7 II. FORMALISM model observables, not unobservable quantities! observables: (physical) observed redshift z obs, position ˆn = (θ, φ) unobservables: (gauge-dependent) redshift z, angular position ŝ =ˆn (δθ, δφ) photon geodesic equation 1 + z obs = (1 + z) 1 + V (z) V (0) ψ(z) + ψ(0) (δr, δθ, δφ) r 0 dr ( ψ φ). 5

8 Effects on Galaxies construct a galaxy fluctuation field: total number of observed galaxies observed volume dv obs given (z obs, ˆn) fluctuation field δ obs = relation to physical number density: number conservation observed number density volume & source effects n obs n obs 1 N tot N tot = n phy dv phy = n obs dv obs n obs = n phy dv phy dv obs 6

9 Galaxy Fluctuation Field standard Newtonian version: general relativistic version: δzχ δ g = bm δz + α χ +2ϕ χ + V C αβ e α e β +3δz χ +2 δr r 5p δd L 2K H z H Yoo, PRD,

10 Galaxy Fluctuation Field standard Newtonian version: δ g = b δ m 1 + z H V r general relativistic version: δzχ δ g = bm δz + α χ +2ϕ χ + V C αβ e α e β +3δz χ +2 δr r 5p δd L 2K it can be computed in any gauges! H z H Yoo, Fitzpatrick, Zaldarriaga, PRD, 2009 Yoo, PRD,

11 III. RESULTS theoretical predictions: new cal. (correct) standard (incorrect) underestimate the observed signals by a factor two at low multipoles 3.7-σ detection, but observed signal is larger by 2 at low multipoles (Ho et al. PRD, 2008) correct predictions standard predictions NVSS + WMAP 8

12 theoretical predictions: new cal. (correct) standard (incorrect) underestimate the observed signals by a factor two at low multipoles 3.7-σ detection, but observed signal is larger by 2 at low multipoles (Ho et al. PRD, 2008) III. RESULTS correct predictions standard predictions NVSS + WMAP Yoo, Fitzpatrick, Zaldarriaga, PRD,

13 Galaxy Power Spectrum matter fluctuation: gauge-dependent ρ m = ρ m (t)[1 + δ m ]= ρ m (z obs )[1 + m δ ] δ m 1+z obs =(1+z)(1 + δz) time slicing (coordinate vs observed redshift) gauge-invariant, observable m δ = δ m 3 δz Bardeen s gauge-invariant m, g m = g = m δ matter rest frame & zero-shear frame gauge-invariance is a necessary but not a sufficient condition for observable quantities Yoo, PRD,

14 Real-Space Matter Power no longer isotropic, neither P S m(k) real-space matter power spectrum, nor P N m (k) P mδ (k, µ k ) P N m (k) P S m(k) P mδ (k ) P mδ (k ) P ψ (k) P v (k) 10

15 Observed Galaxy Power Spectrum largely similar to b 2 P mδ (k, µ k ) (green) unique signature on large scales (ring a bell?) P S m(k) P g (k ) P g (k ) 11

16 Systematic Errors Baryonic Oscillation Spectroscopic Survey (BOSS) can we do more in current surveys? 12

17 Systematic Errors Baryonic Oscillation Spectroscopic Survey (BOSS) can we do more in current surveys? 12

18 Systematic Errors Baryonic Oscillation Spectroscopic Survey (BOSS) can we do more in current surveys? YES, talk to Nico Hamaus (in preparation) 12

19 False Detection misinterpretation as detection of non-gaussianity depending on f NL, systematic errors can be large talk to Tobias Baldauf (in preparation) Correct GR Gaussian case standard f NL =5 13

20 GENERAL RELATIVISTIC DESCRIPTION OF OBSERVED GALAXY POWER SPECTRUM JAIYUL YOO INSTITUTE for THEORETICAL PHYSICS, UNIVERSITY of ZÜRICH Michigan Center for Theoretical Physics, May, 14,