New Probe of Dark Energy: coherent motions from redshift distortions Yong-Seon Song (Korea Institute for Advanced Study)

Transcription

1 New Probe of Dark Energy: coherent motions from redshift distortions Yong-Seon Song (Korea Institute for Advanced Study) 1

2 Future wide-deep surveys Photometric wide-deep survey Spectroscopic wide-deep survey New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 2/30

3 Dark energy study prospects Precision measurements of distance, growth, and curvature: it is desirable for future surveys to provide results of the distance and growth of structure, so that different theoretical models can be discernible. Is dark energy a cosmological constant? : w=-1 even with generalized parameterization of all possibilities, e.g. variation of w, screening effect, induced anisotropy etc. Is dark energy isotropic and homogeneous? : we need examine the distribution, mean, and rms value of w over all the pixels to see. Is acceleration caused by modified gravity instead? : we need at least two different probes, WL and coherent motions. New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 3/30

4 Dark energy study prospects Photometric wide-deep survey Spectroscopic wide-deep survey WL SN BAO SN New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 4/30

5 Beyond standard models With the level of precision available in these surveys, what they tell us about fundamental physics? : whether we can test GR cosmologically, whether we can constrain beyond Standard Model of particle physics. What can a wide deep survey tell us about the basic assumptions behind the standard cosmology? : test cosmological principle (isotropy and homogeneity), and Gaussianity. What are the technical challenges to making these future surveys productive? New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 5/30

6 Beyond standard models: test of GR Photometric wide-deep survey Spectroscopic wide-deep survey G μν = 4πG N T μν Metric Perturbations WL measures Φ-Ψ Energy-Momentum Fluctuations Galaxy-Galaxy correlation Anisotropy Geometrically induced Φ Ψ Poisson equation Modified by mass screening effect We need at least two probes targeting metric and matter fluctuations Euler equation δm θm Continuity eq. Coherent motions YSS, Hollestein, Caldera-Cabral, Koyama 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 6/30

7 Developed techniques Velocity measurements of nearby supernovae Velocity measurements of nearby galaxies Gordon, Land, Slosar (2008) Feldman, Watkins, Hudson (2009) Watkins, Feldman, Hudson (2009) Lavaux, Tully, Mohayaee, Colombi (2010) Analyzed CMB fluctuations on directions of X-ray clusteres Kashlinsky, Atrio-Barandela, Kocevski, Ebeling (2008) Kashlinsky, Atrio-Barandela, Kocevski, Ebeling (2009) Measuring coherent motions from redshift distortions YSS, Pervical (2008) White, YSS, Pervical (2009) YSS, Sabiu, Nichol, Miller (2010) YSS, Sabiu, Kayo, Nichol (2010) New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 7/30

8 Measuring coherent motions using RD Galaxies (or Clusters) measure correlations amongst large scale local inhomogeneities, while the observed distortions in these correlations in redshift space can be used to extract information about peculiar velocities. P s (k,μ) = P gg (k) + 2μ 2 P gθ (k) + μ 4 P ΘΘ (k) Squeezing effect at large scales (Kaiser 1987) Finger of God effect at small sclaes (Jackson 1972) New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 8/30

9 Measuring coherent motions using RD Galaxies (or Clusters) measure correlations amongst large scale local inhomogeneities, while the observed distortions in these correlations in redshift space can be used to extract information about peculiar velocities. P s (k,μ) = P gg (k) + 2μ 2 P gθ (k) + μ 4 P ΘΘ (k) P gθ / P gg P ΘΘ =1 Errors can be estimated using Fisher matrix analysis, F αβ = A k 2 dk dμ dp s (k,μ)/dq α (V eff /P s ) 2 dp s (k,μ)/dq β where q α = (P gg, P ΘΘ ). White, YSS, Percival 2009 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 9/30

10 Estimated errors to decompose P ΘΘ Euclid White, YSS, Percival 2009 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 10/30

11 Realization of decomposition using simulation The Horizon simulation by Teyssier et.al. Time streaming halo caltalogue Medium redshift z=0.8 Total volume 1Gpc 3 /h 3 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 11/30

12 P s (k) from time streaming Halo map P s (k,μ) = P gg (k) + 2μ 2 P gg (k)p ΘΘ (k) + μ 4 P ΘΘ (k) YSS, Kayo 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 12/30

13 P s (k,μ) in polar coordinate P s (k,μ) = P gg (k) + 2μ 2 P gg (k)p ΘΘ (k) + μ 4 P ΘΘ (k) YSS, Kayo 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 13/30

14 Smearing effect of FoG at linear regime P s (k,μ) = P gg + 2μ 2 P gg P ΘΘ + μ 4 P ΘΘ P s (k,μ) = [P gg + 2μ 2 P gg P ΘΘ + μ 4 P ΘΘ ]exp[-(kμσ v ) 2 ] YSS, Kayo 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 14/30

15 Maximum likelihood method of decompostion As P s (k,μ) is given in polar coordinate, we can decompose P ΘΘ from measured spectra in each given bin μ using fitting formulation, χ i 2 = Σ p Σ q [P s ob (k i,μ p ) - P s th (k i,μ p )] Cov -1 pq(k i ) [P s ob (k i,μ q ) - P s th (k i,μ q )] where P s th (k i,μ p ) = P gg (k i ) + 2μ p2 P gg (k i )P ΘΘ (k i ) + μ p4 P ΘΘ (k i ). P s th (k i,μ) = [P gg (k i ) + 2μ p2 P gθ (k i ) + μ p4 P ΘΘ (k i )] exp[-(k i μ p σ v ) 2 ] Scoccimarro 2004 σ v is estimated from P ΘΘ (k i ) at all selected bins, e.g. k i =0.03, 0.05, 0.07, 0.09 h/mpc χ 2 = Σ i Σ p Σ q [P s ob (k i,μ p ) - P s th (k i,μ p )] Cov -1 pq(k i ) [P s ob (k i,μ q ) - P s th (k i,μ q )] YSS, Kayo 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 15/30

16 Measured P ΘΘ from small volume simulation Fisher matrix (unfilled contours) Measurement (filled contours) True velocity is reproduced at k=0.03, 0.05, 0.07 h/mpc The measured errors are consistent with prediction using Fisher matrix analysis YSS, Kayo 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 16/30

17 Strategy to cure non-linear contamination k = 0.09 h/mpc We exclude couple of bins contaminated by non-linear smearing effect YSS, Kayo 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 17/30

18 Result of application cut-off strategy Fitting to all 5 μ bins Fitting to 3 μ bins Detectability can be extended up to k 0.1 h/mpc at the cost of weakened constraint. YSS, Kayo 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 18/30

19 Non-perturbative contribution Two different approaches to formulate redshift distortion effect, 1) streaming model, 2) Kaiser effect, 1) streaming model: formulating FoG effect at smaller scale 2) Kaiser effect: formulating redshift distortion at large scale The limit of streaming model at linear regime was derived in Fisher 1995, and shows the agreement between both approaches. It is interesting to derive FoG effect on redshift distortion at linear regime using streaming model. We make the following assumption, coherent v z in Mpc/h unit << correlation length Then, Desjacques, Sheth 2009; YSS, et.al Prepared P s th (k i,μ) = [P gg (k i ) + 2μ p2 P gθ (k i ) + μ p4 P ΘΘ (k i )] exp[-(k i μ p σ v ) 2 ] New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 19/30

20 Additional correction terms to close theory With the given FoG term, we complete the purturbative effect on the observed spectra where, P s th (k i,μ) = exp[-(k i μ p σ v ) 2 ] [P gg (k i ) + 2μ p2 P gθ (k i ) + μ p4 P ΘΘ (k i ) + A(k,μ) + B(k,μ)] A(k,μ) = kμ dp 3 p z /p 2 [B p (p,k-p,-k) - B p (p,k,-k-p)] B(k,μ) = (kμ) 2 dp 3 p z /p 2 F(p) F(k-p) where B p and F represent bi-spectra and power spectra of the combination of P gθ and P ΘΘ. Taruya, Nishimichi, Saito 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 20/30

21 Measured P s (k,μ) in larger simulation P s (k,μ) = [P gg (k) + 2μ 2 P gg (k)p ΘΘ (k) + μ 4 P ΘΘ (k)] exp[-(kμ p σ v ) 2 ] Preliminary Cut-off kμ=0.05 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 21/30

22 Measured P ΘΘ from large volume simulation P s (k,μ) = [P gg (k) + 2μ 2 P gg (k)p ΘΘ (k) + μ 4 P ΘΘ (k)] exp[-(kμ p σ v ) 2 ] Preliminary New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 22/30

23 Detectability limit of decomposed P ΘΘ Euclid New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 23/30

24 Dark energy study using decomposed P ΘΘ Spectra P ΘΘ are given by, CMB priors for cosmological test with P ΘΘ, Primordial information - amplitude and spectral index Shape of spectra - transfer function We probe dark energy or modified GR using growth factor g Θ, dδ m /dt + θ m /a = 0 dθ m /dt + Hθ m = k 2 Ψ/a k 2 Φ = 3/2 H 02 Ω m δ m /a + k 2 φ Φ = -Ψ + φ (1+3ω BD ) k 2 φ = -3H 02 Ω m δ m /a - M 2 φ YSS 2011 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 24/30

25 BAO using decomposed P gg YSS 2011 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 25/30

26 Coherent combination of BAO and P ΘΘ Cosmological constraints from P ΘΘ are estimated using Fisher matrix analysis, BAO from decomposed P gg is expressed as, YSS 2011 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 26/30

27 Dark energy study prospects: BAO + CM Coherent motions BAO Synergy effect between Coherent motions and BAO YSS 2011 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 27/30

28 Constraint on Φ-Ψ and Ψ using WL and CM YSS, Zhao, Koyama, Nichol, Bacon, Pogosian 2010 Metric Perturbations WL measures Φ-Ψ Energy-Momentum Fluctuations Φ Poisson equation δm Anisotropy Continuity eq. Ψ Euler equation θm PV measures θ and estimates Ψ New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 28/30

29 Beyond standard models: test of GR Synergy effect between Coherent motions and WL 20 times smaller constraints in the future ΔΨ Δ(Φ-Ψ) YSS, Zhao, Koyama, Nichol, Bacon, Pogosian 2010 New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 29/30

30 Conclusion Measurement of coherent motions will take key roles to understand dark energy and to test fundamental physics beyond standard models. We estimate theoretical errors to probe coherent motions from redshift distortions. Fisher matrix formalism for future survey is available. We test detectability of coherent motions using horizon size simulation, and show that we are able to decompose coherent motion power spectra at linear regime. Dark energy study prospect: we combine BAO and coherent motions coherently to enhance the dark energy constraint. Modified gravity test (beyond standard model): measurement of coherent motions is a clean probe of matter perturbation compensating metric perturbation measured by weak lensing. New probe of dark energy / Y.-S. Song / ysong@kias.re.kr 30/30