constraining cosmological parameters using boss data

IntroductionPower Spectrum

BispectrumConclusions

Constraining cosmological parameters using BOSSdata: Power Spectrum and Bispectrum

Hector Gil Marın

Laboratoire de Physique Nucleaire et de Hautes Energies

Rencontres de Moriond 20th March 2016

Rencontres de Moriond 20th March 2016 Constraining cosmological parameters using BOSS data



Outline

1 Introduction

2 Constrains from the BOSS DR12 Power Spectrum multipoles[arXiv:1509.06386] and [arXiv:1509:06373]

3 Constrains from the BOSS DR12 Bispectrum(work in progress)




The BOSS surveyAnisotropy

Introduction: the BOSS survey

Apache Point Observatory (APO) 2.5-m telescope for fiveyears from 2009-2014.

Part of SDSS-III project. BOSS: Baryon OscillationSpectroscopic Survey

Total coverage area about 10,000 square degrees

Two samples with different target selection: LOWZ andCMASS

Two patches in the Northern and Southern Hemisphere

BOSS Galaxies: LRGs.

0.15 ≤ z ≤ 0.43 LOWZ

0.43 ≤ z ≤ 0.70 CMASS

∼ 7 · 105 galaxies in 6Gpc3





LOWZ and CMASS samples

0

1

2

3

4

5

6

7

0.2 0.3 0.4 0.5 0.6 0.7

n(z)

x 1

04 [Mpc

h-1]3

z

LOWZ sample

CMASS sample

The two redshift bins havedifferent target selection.

We treat them as independentgalaxy population with differentgalaxy bias properties.

CMASS has ∼ 3 times the volume that LOWZ

For simplicity we only present the results for CMASS.





Anisotropies: RSD + AP

General picture tell us (at sufficiently large scales) there is not aprivileged observer (Copernican principle). Therefore, the Universewe observe from Earth (or any other random point) must look likeisotrope and homogeneous at large scales.However there are two phenomenon that ’break’ this principle inthe observed data. Both of them relies on how the co-movingdistances are estimated:

1 Redshift space distortions (RSD)

2 Alcock-Paczynski (AP)





Anisotropies: RSD

Kaiser approximation (only for large scales)

P(0) = P(k)[(bσ8)2 +2

3(f σ8)(bσ8) +

1

5(f σ8)2]

P(2) = P(k)[4

3(bσ8)(f σ8) +

4

7(f σ8)2]

but for smaller scales, more complex model is needed.Kaiser (1987)





Anisotropies: AP

An extra source of anisotropy comes from AP-effect, Theco-moving distance to an observed galaxy is given by,

dcomov(z) =

∫ z

0

cdz ′

H(z ′)

where, H(z) = H0

√Ωm(1 + z)3 − Ωm + 1.

By assuming a wrong cosmological model (Ωm) we change theline-of-sight clustering respect to the angular clustering, creating ameasurable anisotropy: constrains H(z) and DA(z)→BAO!Alcock & Paczynski (1979)




ParametrizationMeasurements

RSD Constrains from the Power Spectrum

Goal

To get constrains on f σ8, DA, and H using the shape and theamplitude of P(0) and P(2) in redshift space.

Issues

Galaxy bias may be non-local, non-linear and stochastic

RSD small scale modelling

Dark matter small scales modelling: matter and velocity-fields

Need to include AP parameter to account for inaccuracieswhen assuming Ωm





Galaxy Bias

Galaxies are a biased tracers of DM.

The bias model can be as complex as we want: linear bias,non-linear bias, non-local bias,....

Eulerian non-local bias model (local in Lagrangian space),

δg (x) = b1δ(x)︸︷︷︸linear Eulerian

+

non-linear Eulerian︷︸︸︷1

2b2[δ(x)2] +

1

2[

47(1−b1)︷︸︸︷bs2 ][

tidal tensor︷︸︸︷s(x)2 ]︸︷︷︸

non-local Eulerian

McDonald & Roy 2009





Power Spectrum model

This scheme is applied the real space galaxy power spectrum(Beutler et al 2014)

We use the TNS model for describing the redshift space powerspectrum (Taruya, Nishimichi & Saito 2010),

P(s)g (k , µ) = DP

FoG(k , µ, σPFoG[z ])[Pg ,δδ(k) + 2f µ2Pg ,δθ(k)

+f 2µ4Pθθ(k) + b31A(k, µ, f /b1) + b41B(k, µ, f /b1)]

Pδδ, Pδθ, Pθθ → Dark Matter non-linear models (2-loop RPT)DPFoG → 1-parameter Lorentzian damping term

A,B → TNS functions





Parametrization

The total number of free parameters of the model is,

Bias Parameters: b1, b2

Cosmology Parameters: f , σ8

AP parameters: α‖, α⊥

Fingers-of-God: σFoG

Shot noise amplitude ANoise

8 free parameters.





Parametrization

The total number of free parameters of the model is,

Bias Parameters: b1, b2

Cosmology Parameters: f , σ8

AP parameters: α‖, α⊥→ DA/rs(zd) and H(z)rs(zd)

Fingers-of-God: σFoG

Shot noise amplitude ANoise

8 free parameters → 4 cosmological, 4 “nuissance”





Measurements

0.7 0.8 0.9

1 1.1 1.2

0.01 0.1 0.2

Pda

ta /

Pm

odel

k [h/Mpc]

103

104

105

P(l)

(k)

[(M

pc/h

)3 ]

CMASS (zeff=0.57)

Monopole

Quadrupole

8.7

9

9.3

9.6

9.9

CMASS sample (z=0.57)

DA(z

)/r s

(zd)

P(0)+P(2); kmax=0.23 hMpc-1

12

12.5

13

13.5

14

14.5

15

0.3 0.4 0.5H

(z)r

s(z d

) [1

03 km

s-1]

f(z)σ8(z) 8.7 9 9.3 9.6 9.9

DA(z)/rs(zd)

f σ8(zcmass) = 0.444± 0.038 [f σ8|no−AP = 0.438± 0.021]

H(zcmass)rs(zd) = (13.92± 0.44)× 103kms−1

DA(zcmass)/rs(zd) = 9.42± 0.15





Measurements

We compare the results with other BOSS papers / other redshiftsurveys

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

Chuang et al. ’13

Beutler et al. ’14

Samushia et al. ’14

Sanchez et al ’14

Reid et al. ’14

Alam et al ’15

Gil-Marin ’15

This work

fσ8

CMASS sample

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

fσ8

z

6DFGS

SDSS MGS

SDSS LRG

WiggleZLOWZ

CMASS

VIPERS

Planck + γ=0.420Planck + γ=0.545Planck + γ=0.680





What’s next?

But....

The 2-pt function / Power spectrum is not the end of thestory....

Gravitational evolution of galaxies generates a non-Gaussiancomponent. The full information is spread along higher ordercorrelation function: 3-point, 4-point, ... correlation functions.

Using the 3-pt function / bispectrum in combination with thepower spectrum we can improve the constrains on theseparameters.




Statistical momentsMeasurementConstrains

Introduction: Statistical moments

1 The power spectrum is the Fourier transform of the 2-pointfunction.

〈δk1δk2〉 = (2π)3P(k1)δD(k1 + k2)

It contains information about the clustering.

2 The bispectrum is the Fourier transform of the 3-pointfunction.

〈δk1δk2δk3〉 = (2π)3B(k1, k2)δD(k1 + k2 + k3)

It essentially contains information about the non-Gaussianities:primordial + gravitationally inducedSince is gravitationally sensible → Test of GRIt is essential to break the typical degeneracies between biasparameters, σ8 and f .





Measurement

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

0 50 100 150 200 250 300

∆B /

σ B

Triangle Index

0.4 0.6 0.8

1 1.2 1.4 1.6

Bda

ta/B

mod

el

108

109

B [M

pc/h

]6

CMASS sample (zeff=0.57)

Equilateral

Isosceles

Scalene Bins of ∆k = 6kf

' 350 triangles fork < 0.17h/Mpc

' 600 triangles fork < 0.22h/Mpc

Full Covariance from mocks

SPT + eff Kernels (G-M et al2014) for Bispectrum modelling





Comparing P vs. P + B

How much statistical signal do we gain by adding the Bispectrum?The answer depends on the scales.

Large Scales: few triangle allowed, good modelling

Small Scales: lots of triangles, poor modelling.

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23

σ fσ 8

[%]

kmax [hMpc-1]


P(0) + P(2)

P(0) + P(2) + B(0)

Up to kmax = 0.16 no gain on f σ8.

For kmax = 0.22 hMpc−1 Gain of 2

Systematics of the model grow with kmax.





Constrains at k = 0.17 hMpc−1

8.7

9

9.3

9.6

DA(z

)/r s

(zd)


12 12.5

13 13.5

14 14.5

H(z

)rs(

z d)

[103 k

ms-1

]

0.5

0.6

0.7

0.8

0.4 0.6 0.8 1

σ 8(z

)

f(z)

8.7 9 9.3 9.6DA(z)/rs(zd)

12 13 14

H(z)rs(zd) [103 kms-1]






8.7

9

9.3

9.6

9.9


DA(z

)/r s

(zd)

P(0)+P(2); kmax=0.23 hMpc-1

P(0)+P(2)+B(0); kmax=0.17 hMpc-1

12

12.5

13

13.5

14

14.5

15

0.3 0.4 0.5

H(z

)rs(

z d)

[103 k

ms-1

]

f(z)σ8(z) 8.7 9 9.3 9.6 9.9

DA(z)/rs(zd)

0.4

0.5

0.6

0.7

0.8

0.9

1

0.4 0.5 0.6 0.7 0.8 0.9 1

σ 8(z

eff)

f(zeff)

CMASS sample

DR11 data

DR12 data

Planck15 data

Agreement between P and P+B






8.7

9

9.3

9.6

9.9


DA(z

)/r s

(zd)

P(0)+P(2); kmax=0.23 hMpc-1

P(0)+P(2)+B(0); kmax=0.22 hMpc-1

12

12.5

13

13.5

14

14.5

15

0.3 0.4 0.5

H(z

)rs(

z d)

[103 k

ms-1

]

f(z)σ8(z) 8.7 9 9.3 9.6 9.9

DA(z)/rs(zd)

0.4

0.5

0.6

0.7

0.8

0.9

1

0.4 0.5 0.6 0.7 0.8 0.9 1

σ 8(z

eff)

f(zeff)

CMASS sample

DR11 data

DR12 data

Planck15 data

Agreement between P and P+B




Conclusions

We have measured the power spectrum monopole (isotropic)and quadrupole (anisotropic) signal from the BOSS DR12galaxies.

We have constrained cosmological parameters: the growth ofstructure of the Universe, f σ8, Hubble Parameter H(z) andthe angular diameter distance DA.

We have shown how by adding the bispectrum signal on thetop of the power spectrum multipoles, we can reducesignificantly the statistical error bars and break the degeneracybetween f and σ8.




Extra slides

0.85

0.9

0.95

1

1.05

1.1

1.15

0 100 200 300 400 500 600 700 800

B /

Bno

sys

Triangle index

CMASS sample

ki<0.03 hMpc-1

ki>0.17 hMpc-1

k1>0.03 hMpc-1 & k3<0.17 hMpc-1




Extra slides

[rij]CMASS

0 50 100 150 200 250 300 350

0

50

100

150

200

250

300

350

-1

-0.5

0

0.5

1




Extra slides

-2-1 0 1 2 3 4 5

0 50 100 150 200 250 300

∆B /

σ B

Triangle Index

108

109

B [M

pc/h

]6


MD-Patchy Mocks

Data

MD-Patchy mean

QPM mean




Extra slides

0.1

1

10

50

0 50 100 150 200 250 300

σ B /

B(0

) data

[%]

Triangle Index

CMASS sample

statistical errorssystematic correction




Extra slides

0.35

0.4

0.45

0.5

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23

fσ8

kmax [hMpc-1]

0.92 0.94 0.96 0.98

1 1.02 1.04 1.06

α ||

0.94 0.96 0.98

1 1.02 1.04 1.06

α ⊥

CMASS data (zeff=0.57)




Extra slides

0.94 0.96 0.98

1 1.02 1.04

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23

fσ8

/ [fσ

8]tr

ue

kmax [hMpc-1]

0.96

0.98

1

1.02

1.04

α || /

[α||]

true

0.96 0.98

1 1.02 1.04 1.06 1.08 1.1

α ⊥ /

[α⊥]tr

ue

CMASS mocks

MD-Patchy

Inter-bias Haloes

High-bias Haloes

Low-bias Haloes


constraining cosmological parameters using boss data

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