Robust cosmological constraints from

SDSS-III/BOSS galaxy clustering

Chia-Hsun Chuang (Albert)

IFT- CSIC/UAM, Spain

SDSS-III/BOSS

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)

Baryon Acoustic Oscillations

Planck

Baryon Acoustic Oscillations

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)

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)σ8(z)

Reconstructed number density field of the galaxy sample

Measure DV(z)/rs ( or H(z)rs & DA(z)/rs) with

higher precision

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

Dark energy model independent measurements

• Measured parameters: H(z), DA(z),

f(z)σ8(z), Ωmh2, , 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.

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).

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

MCMC analysis

• Software: CAMB, CosmoMC

• 9 parameters explored:

– H, DA, Ωmh2, β, and b σ8 are well constrained

– Ωbh2 (±10σPlanck), ns (±10σPlanck), f (0.5~1), and

σv(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)

Measured and derived parameters

Chuang et al. 2013

Normalized covariance matrix (15 x 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.

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).

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 Ωmh2 as our

robust measurements since it is sensitive to

the overall shape. Also, we rotate all the

measurements to be independent of Ωmh2.

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

Measured and derived parameters

Chuang et al. 2013

Assuming a Dark Energy Modelhttp://members.ift.uam-csic.es/chuang/BOSSDR9singleprobe/

• E.g., ΛCDM (Ωm, H0, σ8)Chuang et al. 2013 (arXiv:1312.4889)

Assume ΛCDM

Assume non-flat ΛCDM

Chuang et al. 2013 (arXiv:1312.4889)

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

Assume oΛCDMChuang et al. 2013 (arXiv:1312.4889)

Conclusion

• We obtained the robust measurements of H(z), DA(z),

f(z)σ8(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.

EZmocks: extending the Zel'dovich approximation to generate mock galaxy

catalogues with accurate clustering statistics (Chuang and Kitaura et al. 2014)

Power spectrum

EZmocks: extending the Zel'dovich approximation to generate mock galaxy

catalogues with accurate clustering statistics (Chuang and Kitaura et al. 2014)

Correlation function

Bispectrum

Backup slides

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.

Covariance matrix & χ2

• Using 600 mock catalogs from the second-order

Lagrangian Perturbation Theory (Manera et al.

(2012))

Rescaling theoretical correlation function with DV(z)

rescaling

S1

S2

αS1αS2

Fiducial model New model

Rescaling theoretical correlation function with DV(z)

where

2D correlation function

σ

π

Measure H(z) and DA(z) with 2D correlation function

• Rescaling theoretical correlation

function with H(z) and DA(z) instead

of DV(z)

2D rescaling

σ1

π2

π1

βσ2

γπ1γπ2

σ2

βσ1

Model

• Anisotropic dewiggle model

(Eisenstein, Seo, and White 2007)

Chuang et al. 2013 (arXiv:1312.4889)

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)

Model

• Anisotropic dewiggle model

(Eisenstein, Seo, and White 2007)

• Linear redshift distortion (Kaiser

approximation)

Chuang et al. 2013 (arXiv:1312.4889)

Model

• Anisotropic dewiggle model (Eisenstein,

Seo, and White 2007, Crocce &

Scoccimarro 2006, Matsubara 2008)

• Linear redshift distortion (Kaiser

approximation)

• Pairwise velocity dispersionChuang et al. 2013 (arXiv:1312.4889)

Assuming wCDMChuang et al. 2013 (arXiv:1312.4889)

The strong power of anisotropic information on constraining dark

energy (wCDM)

Chuang et al. 2013 (arXiv:1312.4889)