Constraining cosmological parameters with BAO and RSD from BOSS & eBOSS galaxy clustering

datasetsHéctor Gil-Marín (Institute Lagrange de Paris Fellow, LPNHE Sorbonne University)

CosmoBack: From inhomogeneous gravity to cosmological back-reaction Marseille, 31st May 2018

Probes to test Dark Energy on late-time Universe

• Standard Candle Supernovae

• Weak lensing

• Cluster counting

• Standard Ruler BAO & RSD

Observe dark matter tracers with high precision redshift covering a large area/volume of the sky

How?

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Cosmological Standard Model

Main Goal of redshift surveys: BAO & RSD

• Standard Ruler BAO & RSD

Growth of structure: Ratio monopole to quadrupole ~ fσ8

BAO peak position: in monopole ~ (DA2/H)1/3 / rs DV / rs

BAO relative peak position: monopole, ‘quadrupole’ ~ DAH

fσ8(z) H(z)rs DA(z)/rs ( DV/rs )Cosmological Parameters

non-Cosmological ParametersGalaxy bias physics: b1σ8 b2σ8 σFoG …..

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

DR14 footprint for the quasar sampleDR12 footprint for the LRG sample

BOSS & eBOSS spectroscopic surveys

Area = 9376 deg2 Area = 2112.9 deg2 0.2<z<0.5

0.4<z<0.60.5<z<0.75

3overlapping z-bins

0.8<z<2.2Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

~106 LRG targets~1.5·105 quasar targets

The redshift survey catalogues deliver: angles and redshifts for each galaxy

r(z) = cdz 'H (z ',Ωm )0

z

∫

δ (r1)δ (r2 ) = ξ r1 − r2( ) δ (k1)δ (k2 ) = P(k1)δD k1 + k2( )

Clustering strength: Quantify number of pairs over a uniform random distribution: correlation function, ξ(R), or Power Spectrum, P(k)

Clustering of Tracers: What do we measure?

H (z,Ωm ) = H0 Ωm (1+ z)3 +1−Ωm

3D galaxy maps

… and higher order functions, such as bispectrum.

Credit: Anand Raichoor

FLRW Universe

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Baryonic Acoustic Oscillation peakUsing BAO/RSD as a standard ruler, galaxies, Lya, … measure, • [DA(z)2/H(z)]1/3/rs (isotropic) • DA(z)H(z) (anisotropic) • fσ8(z) (anisotropic) at the redshift of the tracer, z With this, we can measure DA(z)/rs and H(z)rs

rs given by CMB / BBN

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

see Jim’s Talk

Vp

!"!= x! !V! + x! ⊥V⊥

• Universe assumed isotropic and homogeneous • RSD: Enhancement / reduction of the clustering along the

line-of-sight (LOS) direction due to peculiar velocities (Kaiser 1987)

not detected

ztrue

vp

vp

LOS

vy

vy

vx

vx

line-

of-s

ight

dire

ctio

n Actual Shape

Observed Shape

over-density

1. Hubble flow2. Coherent with growth of structure

Redshift Space Distortions

zobs = ztrue ⊕ zpec ≡ (1+ ztrue )× (1+ zpec )⎡⎣ ⎤⎦ −1

f (z) = Ωm (z)γ

logarithmic growth of structure

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

• Universe assumed isotropic and homogeneous • AP effect: Anisotropy induced by transforming redshifts

into coming distances assuming a wrong cosmology

Both transverse and longitudinal modes are modified by Ωm

Radial distance Angular diameter distance

ΔθΔr

Δr

Δr!(z1, z2;Ωm ) =cdz '

H0 Ωm (1+ z ')3 +1−Ωm

z1

z2∫ ≈ cΔzH (z ,Ωm )

Δr⊥ (θ1,θ2;z,Ωm ) = Δθ cdz 'H (z ',Ωm )0

z

∫

Alcock-Paczynski effect

cluster is modified along both directionsHector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

1

2

3

4

5

6

0.01 0.1

Nor

mal

ized

Pow

er

k

~ 1αV

~ 1αV

Physical Interpretation αV~ (DA2/H)1/3 / rs

Monopole

Quadrupole

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

P(µ2 ) ≡ P(0) + 2

5P(2)

1

2

3

4

5

6

7

8

0.01 0.1

Nor

mal

ized

Pow

er

k

Physical Interpretation αε~ DAH

Quadrupole

Monopole

μ2-moment

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

• These 3 effects are degenerated for a power law-like power spectrum

• Only when we have a scale of reference, we can constrain them independently

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Pow

er

wave number

observed range

RSD

AP

Physical InterpretationIsotropic dilation Alcock-PaczynskiRSD

Power Spectrum Correlation Function

Type of analyses: • RSD (full shape) vs. BAO, • pre-recon vs. post-recon, • configuration space vs. Fourier space

LRGs BAO/RSD from BOSS

Alam et al. 2016

0.2<z<0.50.4<z<0.60.5<z<0.75

3overlapping z-bins

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Alam et al. 2016

+GR

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

LRGs BAO/RSD from BOSS

0.2<z<0.50.4<z<0.60.5<z<0.75

3overlapping z-bins• Good Agreement with Planck+GR • (!) Middle redshift bin point correlated • First time 1% precision BAO measurement

(reconstruction)

-4-3-2-1 0 1 2 3 4

0 0.10 0.20 0.30 0.40

∆P / σ P

k [hMpc-1]

-400

-200

0

200

400

600

800

1000kP

(k) [

Mpc

/h]2

DR14Q 0.8<z<2.2

MonopoleQuadrupole

Hexadecapole

quasar BAO/RSD from eBOSS

HGM et al. 2018

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Significance of BAO peak

• 3σ detection • In good agreement with Planck+GR • DV(z=1.52)=3843 147 Mpc (3.8%)±

Ata et al. 2017

Correlation Function

quasar BAO/RSD from eBOSS

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

HGM et al. 2018

BOSS gal. DR12 BOSS Ly-α. DR12

eBOSS quasars DR14

0.85 0.9

0.95 1

1.05 1.1

1.15

0.1 0.5 1.0 1.5 2.0 2.5

(DA/

r s) /

(DA/

r s)Pl

anck

z

0.8 0.85

0.9 0.95

1 1.05

1.1 1.15

1.2

Hr s

/ (H

r s)Pl

anck

0.3 0.4

0.5

0.6 0.7

0.8fσ

8(z)

MGS DR7 SDSS-IIBOSS LRGs DR12 SDSS-IIIBOSS Ly-α DR12 SDSS-III

eBOSS quasars DR14 SDSS-IV

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Cosmological Interpretation

GR & ΛCDM assumed

0

0.2

0.4

0.6

0.8

1

60 62 64 66 68 70 72 74 76

Ωm

0

H0 (rs/rsfid)

H0 = 73.0 ±1.8

0

0.2

0.4

0.6

0.8

1

1.2

60 62 64 66 68 70 72 74 76

ΩΛ

H0 (rs/rsfid)

DA(z), H(z), fσ8(z) from BOSS galaxies / eBOSS quasars

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

flat ΛCDM

ΩΛ

Ωm0

BOSS galaxieseBOSS quasars + BOSS galaxies

eBOSS quasars + BOSS galaxies + Planck

HGM et al. 2018Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Cosmological Interpretation

BAO Systematics RSD systematics

Impact of potential systematics

• Very robust! • (barely not affected by bg, non-

linearities, obs. systematics)

• ~0.1% non-linear shift at z=1.5 (Blas et al. 2016)

• Relative velocity between DM & gal. (Slepian et al. 2016, bv<0.01)

• Reconstruction assumptions (bias and f) • 2pcf, 3pcf, …, BAO should contain

the same BAO information than post-recon without f or bias assumptions

• Model dependent (PT, shell crossing) A. Galaxy bias model B. DM modelling C. RSD modelling

• Tidal alignments (Hirata 2009; Martens et al. 2018) • Observational selction of galaxies

depending on their environment

• failures & collisions (camera sys.), but corrected by weighting schemes

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille

Summary

• BOSS measured H(z)rs in the range 0.2<z<0.75 using LRGs (high density)

• First results from eBOSS quasars measuring H(z)rs in the range 0.8<z<2.2

• More eBOSS data coming in the next 1.5yr (ELG, LRG, quasars + Lyα): errors of quasars to ~1/2, measurements at z~0.75 from LRGs + ELGs

• Results strongly support LCDM+Planck (Tension with local H0 measurement with SN+Cosmic Ladder)

• (known) Uncorrected systematics not important for current statistical precision, but some of them need to be better controlled for future surveys.

• DESI will deliver more precise results within 5yr from now.

Hector Gil Marin 31st May 2018 Cosmoback @ LAM, Marseille