Statistical challenges in the Lyman- forest Andreu Font-Ribera - - PowerPoint PPT Presentation

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Statistical challenges in the Lyman- forest Andreu Font-Ribera - - PowerPoint PPT Presentation

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Your Name and Collaborators Statistical challenges in the Lyman- forest Andreu Font-Ribera Graphic: Anze Slozar STFC Ernest Rutherford Fellow at University College London In collaboration with Pat McDonald (LBL) and An e Slosar (BNL) 1

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Graphic: Anze Slozar

Your Name and Collaborators

1

Statistical challenges in the Lyman-α forest

Andreu Font-Ribera STFC Ernest Rutherford Fellow at University College London

In collaboration with Pat McDonald (LBL) and Anže Slosar (BNL)

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 2

Redshift Surveys

Look back time (billion years)

BOSS Lyα forest 160k spectra 2.0 < z < 3.5 BOSS galaxies 1.3M spectra 0.2 < z < 0.7

Overdensity Underdensity

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 3

Redshift Surveys

Look back time (billion years)

BOSS Lyα forest 160k spectra 2.0 < z < 3.5 BOSS galaxies 1.3M spectra 0.2 < z < 0.7

Overdensity Underdensity

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest

Outline

  • Baryon Acoustic Oscillations in the Lyman-α (Lyα) forest
  • Introduction to Lyα surveys
  • BAO results from BOSS Lyα
  • BAO forecasts for DESI Lyα
  • Small scale clustering of the Lyα forest
  • Opportunities (neutrinos, running, warm dark matter)
  • State of the art (one-dimensional power spectrum)
  • Statistical challenges (three-dimensional clustering)

4

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 5

The Lyman-α forest

Credits: Andrew Pontzen

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 6

The Lyman-α forest

fq(λ) = Cq(λ)Fq(λ)

λ = λα(1 + z)

Observed flux Transmitted fraction Quasar continuum Absorption redshift Observed wavelength LyaF wavelength (121.6 nm)

δF (x) = F(x) − ¯ F ¯ F

Flux fluctuations in pixels trace the density along the line of sight to the quasar

440 460 480 500 520 540 ! (nm) !5 5 10 15 20 flux [10!17 erg s!1 cm!2 A!1]

Method 1 Method 2

Quasar Continuum x Mean Flux

1st step: from observed flux to cosmological fluctuations

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest

Outline

  • Baryon Acoustic Oscillations in the Lyman-α (Lyα) forest
  • Introduction to Lyα surveys
  • BAO results from BOSS Lyα
  • BAO forecasts for DESI Lyα
  • Small scale clustering of the Lyα forest
  • Opportunities (neutrinos, running, warm dark matter)
  • State of the art (one-dimensional power spectrum)
  • Statistical challenges (three-dimensional clustering)

7

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 8

BOSS Lyman-α BAO

Gas Quasar Quasar

r

Gas Gas Quasar Quasar

r

Two independent ways of measuring the BAO scale

Bautista et al. (2017) du Mas des Bourboux (2017) —— DR12 ——

1˚ A ∼ 70 km s−1 ∼ 0.7 h−1 Mpc

1 deg ∼ 70 h−1 Mpc

Lyα auto-correlation Lyα-quasar cross-correlation

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 9

BOSS Lyman-α BAO

Two independent ways of measuring the BAO scale

Bautista et al. (2017) du Mas des Bourboux (2017) —— DR12 ——

Lyα auto-correlation Lyα-quasar cross-correlation

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 10

Dark Energy is now detected from BAO data alone

In a flat ΛCDM model BAO Planck

Combined BOSS BAO

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest

Outline

  • Baryon Acoustic Oscillations in the Lyman-α (Lyα) forest
  • Introduction to Lyα surveys
  • BAO results from BOSS Lyα
  • BAO forecasts for DESI Lyα
  • Small scale clustering of the Lyα forest
  • Opportunities (neutrinos, running, warm dark matter)
  • State of the art (one-dimensional power spectrum)
  • Statistical challenges (three-dimensional clustering)

11

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 12

Mayall 4m Telescope Kitt Peak (Tucson, AZ)

Readout 
 & Control

  • 5000 fibers in robotic actuators
  • 10 fiber cable bundles
  • 3.2 deg. field of view optics
  • 10 spectrographs

Dark Energy Spectroscopic Instrument

Scheduled to start in 2019 Increase BOSS dataset by an

  • rder of magnitude
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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 13

Mayall 4m Telescope Kitt Peak (Tucson, AZ)

Readout 
 & Control

  • 5000 fibers in robotic actuators
  • 10 fiber cable bundles
  • 3.2 deg. field of view optics
  • 10 spectrographs

Dark Energy Spectroscopic Instrument

Scheduled to start in 2019 Increase BOSS dataset by an

  • rder of magnitude

Lens in cell, UCL, March 2018

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 14

Dark Energy Spectroscopic Instrument Expansion rate

Planck prediction

Acceleration Deceleration

Redshift

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 15

Dark Energy Spectroscopic Instrument Expansion rate

DESI projections (Font-Ribera++ 2014b)

Planck prediction

Acceleration Deceleration

Redshift

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest

Outline

  • Baryon Acoustic Oscillations in the Lyman-α (Lyα) forest
  • Introduction to Lyα surveys
  • BAO results from BOSS Lyα
  • BAO forecasts for DESI Lyα
  • Small scale clustering of the Lyα forest
  • Opportunities (neutrinos, running, warm dark matter)
  • State of the art (one-dimensional power spectrum)
  • Statistical challenges (three-dimensional clustering)

16

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 17

Small scale clustering

Lyman-α forest offers a unique window to study small scale clustering Combined with CMB, it allows us to study:

  • shape of primordial P(k)
  • dark matter properties
  • neutrino mass

Late time Early time Small scales Large scales

CMB Lyman-α Forest Weak Lensing Spectroscopic Galaxies Photometric Galaxies CMB Lensing

0 1 2 Redshift 5 1100 1000 100 Mpc 10 1

Future 21cm

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 18

Small scale clustering

Flux correlations (P1D or P3D) Quasar spectra Estimator Density power spectrum Hydrodynamical simulations Likelihood Cosmo params (neutrino mass) Planck (+ others)

MCMC

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 19

Small scale clustering

Flux correlations (P1D or P3D) Quasar spectra Estimator Density power spectrum Hydrodynamical simulations Likelihood Cosmo params (neutrino mass) Planck (+ others)

MCMC

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest

Outline

  • Baryon Acoustic Oscillations in the Lyman-α (Lyα) forest
  • Introduction to Lyα surveys
  • BAO results from BOSS Lyα
  • BAO forecasts for DESI Lyα
  • Small scale clustering of the Lyα forest
  • Opportunities (neutrinos, running, warm dark matter)
  • State of the art (one-dimensional power spectrum)
  • Statistical challenges (three-dimensional clustering)

20

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 21

Estimators: 1D P(k)

1D correlations, one skewer at a time (Palanque-Delabrouille et al. 2013)

Line of sight (1D) wavenumber ~ 2 h/Mpc ~ 0.1 h/Mpc

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest

Outline

  • Baryon Acoustic Oscillations in the Lyman-α (Lyα) forest
  • Introduction to Lyα surveys
  • BAO results from BOSS Lyα
  • BAO forecasts for DESI Lyα
  • Small scale clustering of the Lyα forest
  • Opportunities (neutrinos, running, warm dark matter)
  • State of the art (one-dimensional power spectrum)
  • Statistical challenges (three-dimensional clustering)

22

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 23

Estimators: 3D P(k)

  • Good to have an alternative way to study BAO
  • Constraint cosmology from the Lyα clustering, beyond BAO

(DESI Lyα forecasts dominated by P3D, not P1D) Motivation However, current 3D studies in BOSS/eBOSS only try to measure BAO 1D analyses have used both FFT / Pseudo-Cl and Maximum Likelihood

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 24

Estimators: 3D P(k)

Likelihood-based

L(p) ' L(p0) + dL dpi pi + 1 2 d2L dpidpj pipj + ... ⌘ L(p0) + L,ipi + 1 2L,ijpipj + ...

L(|p) / det (C)−1/2 exp  1 2tC−1

  • = exp L ,

pmax

i

= p0

i L−1 ,ij L,j ,

L,i = 1 2tC−1S,iC−1 1 2Tr ⇥ C−1S,i ⇤

L Fij ⌘ hL,iji = 1 2Tr ⇥ C−1S,iC−1S,j ⇤

Optimal Quadratic Estimator

  • Can’t evaluate by brute force (roughly a billion correlated pixels)
  • We need to make controlled approximations for speed
  • Assume uncorrelated skewers (block-diagonal covariance)
  • Rotate data into eigenvectors of response matrices
  • Use special parameterization, change variables later
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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 25

Estimators: 3D P(k)

  • Off-diagonal covariance
  • low-k line of sight modes

(continuum errors) spread over all scales

  • Funky window function

in transverse direction

  • Non-stationary field

(z-evolution) Configuration or Fourier space? Cross-spectrum (hybrid) 1D power is just one of the bins of the cross-spectrum with

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 26

Measurement from 40 mock realizations of BOSS

Estimators: 3D P(k)

JCAP (2018) 1710.11036v2

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 27

Summary

BAO in the Lyα forest

  • 2% measurement at z~2.3 (quasars and the Lyman-α forest)
  • BOSS Ly-α showed the forest is ready for precision cosmology
  • DESI will represent an order of magnitude jump in precision

Small scale clustering of the Lyα forest

  • Ly-α offers a unique window to small scales
  • Strong constraints on warm dark matter, neutrinos or running
  • Several statistical and computational challenges
  • Many interesting projects, very few people working on it!
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Extra slides

28

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 29

BAO and the H0 tension

Riess et al. (2016)

Addison et al. (2017)

Planck + LCDM predicts value of H0 lower than that from local expansion (Riess et al. 2016) BAO + LCDM constraint Ωm and H0 rs (sound horizon, size of ruler) With BBN prior on Ωb we can break degeneracy and measure H0 from BAO

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Oxford, April 19th 2018 Andreu Font-Ribera - Statistical challenges with the Lyman-⍺ forest 30

Snowmass report (2014)

Massive neutrinos are hot dark matter, do not cluster on small scales Comparing the power

  • n large and small scales

we can constraint neutrino masses Best constraints from Planck + BOSS Lyα Σmν < 0.12 eV (95%)

(Palanque-Delabrouille++ 2015)

Small scale clustering