1. Robust cosmological constraints from SDSS-III/BOSS galaxy clustering Chia-Hsun Chuang (Albert) IFT- CSIC/UAM, Spain

2. SDSS-III/BOSS

3. BOSS at a glance Dark time observations from Fall 2009 - Spring 2014 (Mar 31) Final data release (DR12) in Dec. 2014 1,000-fiber spectrograph, resolution R~2000 Wavelength: 360-1000 nm 10,200 square degrees (~quarter of sky) Redshifts of 1.35 million luminous galaxies to z = 0.7 Lyman-α forest spectra of 230,000 quasars (160,000 redshifts > 2.15)

4. Baryon Acoustic Oscillations Planck

5. Baryon Acoustic Oscillations

6. Galaxy sample 690,827 galaxies from SDSS-III BOSS Data Release 11 CMASS (Complete stellar MASS) sample (z=0.43~0.7) 313,780 galaxies from SDSS-III BOSS Data Release 11 LOWZ (low redshift) sample (z=0.15~0.43)

7. Extracting cosmological information from the galaxy clustering Measure Power spectrum or correlation function from: number density field of the galaxy sample Measure H(z)rs, DA(z)/rs, and f(z)σ 8 (z) Reconstructed number density field of the galaxy sample Measure DV(z)/rs ( or H(z)rs & DA(z)/rs) with higher precision

8. Data: monopole and quadrupole from BOSS DR11 CMASS and LOWZ sample (Chuang et al. 2013)

9. Dark energy model independent measurements Measured parameters: H(z), D A (z), f(z)σ 8 (z), Ω m h 2,, β Without assuming dark energy model or curvature – one can use our results to obtain the constraints of the parameters of given dark energy models.

10. Covariance matrix Constructed by using 600 mock catalogues for CMASS (2LPT, see Manera et al. 2013) and 1000 mock catalogues for LOWZ (2LPT, see Manera et al. 2014) For DR12, BOSS will switch to PATCHY mocks (developed by our group, see Kitaura et al. 2013) and/or QPM mocks (White et al. 2013). A new methodology, EZmock, has also been developed by our group (see Chuang et al. 2014).

11. Theoretical Model based on CMB and galaxy formation The well fitted and simple models have following properties: – Adiabatic initial condition – Cold dark matter (CDM) – No early-time dark energy – No clustering of dark energy

12. MCMC analysis Software: CAMB, CosmoMC 9 parameters explored: – H, D A, Ω m h 2, β, and b σ 8 are well constrained – Ω b h 2 (±10σ Planck ), n s (±10σ Planck ), f (0.5~1), and σ v (0~300km/s) 36 data bins (monopole+quadrupole, 56<s<200 Mpc/h, bin size = 8 Mpc/h) Chuang et al. 2013 (arXiv:1312.4889)

13. Measured and derived parameters Chuang et al. 2013

14. Normalized covariance matrix (15 x 15)

15. To be Robust: minimize the systematic bias from priors No CMB priors or fixing values from CMB – one can combine our measurements with CMB or other data sets using CMB priors.

16. To be Robust: Use the scale range of which the model is well understood The model is constructed from linear theoretical model + nonlinear correction, since we are using quasi-linear scales (i.e. 56 < s < 200 Mpc/h).

17. To be Robust: drop the measurements which are easily effected by observational systematics. The overall shape of monopole is sensitive to many observational systematics (e.g. stars, seeing, etc.). We do not include Ω m h 2 as our robust measurements since it is sensitive to the overall shape. Also, we rotate all the measurements to be independent of Ω m h 2.

18. Data: monopole and quadrupole from BOSS DR11 CMASS and LOWZ sample (Chuang et al. 2013)

19. Measured and derived parameters Chuang et al. 2013

20. Assuming a Dark Energy Model http://members.ift.uam-csic.es/chuang/BOSSDR9singleprobe/ E.g., ΛCDM (Ω m, H 0, σ 8 ) Chuang et al. 2013 (arXiv:1312.4889)

21. Assume ΛCDM Assume non-flat ΛCDM Chuang et al. 2013 (arXiv:1312.4889)

22. Assume wCDM Chuang et al. 2013 (arXiv:1312.4889)

23. Assume oΛCDM Chuang et al. 2013 (arXiv:1312.4889)

24. Conclusion We obtained the robust measurements of H(z), D A (z), f(z)σ 8 (z) from SDSS-III/BOSS DR11 CMASS or LOWZ (without assuming dark energy model and curvature). Our methodology can be applied on the current and future large- scale galaxy surveys (e.g. eBOSS, BigBOSS, and Euclid) to obtain single-probe cosmological constraints, which will provide a robust and convenient way to perform a joint data analysis with other data sets.

25. EZmocks: extending the Zel'dovich approximation to generate mock galaxy catalogues with accurate clustering statistics (Chuang and Kitaura et al. 2014) Power spectrum

26. EZmocks: extending the Zel'dovich approximation to generate mock galaxy catalogues with accurate clustering statistics (Chuang and Kitaura et al. 2014) Correlation function

27. Bispectrum

28. Backup slides

29. Observed correlation function 1.Convert the redshifts to comoving distances with a fiducial model 2.Minimum variance correlation function estimator(Landy & Szalay 1993): where DD, DR, and RR represent the normalized data-data, data- random, and random-random pair counts respectively in a distance range.

30. Covariance matrix & χ 2 Using 600 mock catalogs from the second-order Lagrangian Perturbation Theory (Manera et al. (2012))

31. Rescaling theoretical correlation function with D V (z)

32. rescaling S1 S2 α  S1 α  S2 Fiducial model New model

33. Rescaling theoretical correlation function with D V (z) where

34. 2D correlation function σ π

35. Measure H(z) and D A (z) with 2D correlation function Rescaling theoretical correlation function with H(z) and D A (z) instead of D V (z)

36. 2D rescaling σ1 π2 π1 β  σ2 γ  π1 γ  π2 σ2 β  σ1

37. Model Anisotropic dewiggle model (Eisenstein, Seo, and White 2007) Chuang et al. 2013 (arXiv:1312.4889)

38. Anisotropic dewiggle model (nonlinear correction in z-space at BAO scales) The model is validated by Samushia et al. (2012) using N- body simulations. The computation of the model is speeded up by Chuang and Wang (2013) (arXiv:1209.0210)

39. Model Anisotropic dewiggle model (Eisenstein, Seo, and White 2007) Linear redshift distortion (Kaiser approximation) Chuang et al. 2013 (arXiv:1312.4889)

40. Model Anisotropic dewiggle model (Eisenstein, Seo, and White 2007, Crocce & Scoccimarro 2006, Matsubara 2008) Linear redshift distortion (Kaiser approximation) Pairwise velocity dispersion Chuang et al. 2013 (arXiv:1312.4889)

41. Assuming wCDM Chuang et al. 2013 (arXiv:1312.4889)

42. The strong power of anisotropic information on constraining dark energy (wCDM) Chuang et al. 2013 (arXiv:1312.4 889)