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
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