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N o n - l i n e a r b a y e s i a n i n f e r e n c e o f c o s m i c f e l d s i n S D S S 3 a n d 2 M + + Guilhem Lavaux (IAP/CNRS) and Aquila Consortium Statistical Challenge for large-scale

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N

  • n
  • l

i n e a r b a y e s i a n i n f e r e n c e

  • f

c

  • s

m i c f e l d s i n S D S S 3 a n d 2 M + +

Guilhem Lavaux (IAP/CNRS)

and Aquila Consortium

Statistical Challenge for large-scale structure in the era of LSST (Oxford 2018) Aquila consortium (https://aquila-consortium.org)

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Outline Outline

T h e s t a t i s t i c a l f r a m e w

  • r

k T h e 2 M + + c

  • m

p i l a t i

  • n

( p r e s e n t a t i

  • n

, c l u s t e r s , v e l

  • c

i t y f e l d s , a p p l i c a t i

  • n

s ) S D S S 3 B O S S ( m

  • r

e m

  • d

e l i n g c h a l l e n g e s , d e n s i t y f e l d ) C

  • n

c l u s i

  • n
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From theory to observations... From theory to observations...

Model Observations

Perfect Complete description Full knowledge of physics Did I say perfect ? Great but messy We do not understand the physics Systematics not fully known Good attempt by observers to seemingly make our life easier end up bad Various hacking to make sense of data

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From theory to observations... From theory to observations...

Model Observations

Perfect Complete description Full knowledge of physics Did I say perfect ? Great but messy We do not understand the physics Systematics not fully known Good attempt by observers to seemingly make our life easier end up bad

BORG3

Still far too perfect though… (see later)

Another perspective to automatically solve this problem: see Tom Charnock’s talk

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The BORG3 inference framework The BORG3 inference framework

Initial conditions

Jasche et al. (2010), Jasche & Wandelt (2013), Lavaux & Jasche (2016), Jasche & Lavaux (2017, 2018)

Observations Encode survey systematic effects with expansions: Forward description Adjoint gradient

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BORG-PM Performance aspect BORG-PM Performance aspect

Number of cores 700 70 10 100 Time (seconds) Hyperthreading BORG-(2)LPT is ~20 times faster

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A p p l i c a t i

  • n

t

  • 2

M + + g a l a x y c

  • m

p i l a t i

  • n

: D e t a i l e d d y n a m i c a l m

  • d

e l i n g

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The 2M++ galaxy compilation The 2M++ galaxy compilation

0 Mpc/h Galaxy distribution SDSS 6dF 2MRS 250 Mpc/h Redshift completeness

Lavaux & Hudson (MNRAS, 2011)

~70 000 galaxies

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Inferred density fields Inferred density fields

Void Mean Clusters

Higher error Ensemble average density fields at z=0

Jasche & Lavaux (2018, in prep.)

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Performance aspect (2): burnin Performance aspect (2): burnin

Jasche & Lavaux (2018, in prep.)

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Initial condition powerspectrum Initial condition powerspectrum

Initial conditions Post PM simulation

Jasche & Lavaux (2018, in prep.)

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Virgo cluster Virgo cluster

Virgo center ~30 Mpc/h

Jasche & Lavaux; Lavaux & Jasche; Peirani, Lavaux & Jasche (2018, in prep.)

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Coma dynamical properties Coma dynamical properties

Jasche & Lavaux; Lavaux & Jasche; Peirani, Lavaux & Jasche (2018, in prep.)

Coma center

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Coma dynamical properties Coma dynamical properties

Jasche & Lavaux; Lavaux & Jasche; Peirani, Lavaux & Jasche (2018, in prep.)

Zoom simulation on Coma (~250 Mpart in zoom)

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Shapley concentration Shapley concentration

Lavaux & Jasche (2018, in prep.)

~60 Mpc/h Shapley center Single realisation density

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Shapley concentration Shapley concentration

Lavaux & Jasche (2018, in prep.)

~60 Mpc/h Shapley center Ensemble average density

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Inferred velocity fields Inferred velocity fields

Higher error 0 km/s 800 km/s

Infall Outfall

  • 400 km/s

+400 km/s

Jasche & Lavaux (2018, in prep.)

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Velocity field and Hubble constant Velocity field and Hubble constant

Mean error on Hubble measurement using tracers from observed large scale structures

Jasche & Lavaux (2018, in prep.)

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A p p l i c a t i

  • n

t

  • S

l

  • a

n D i g i t a l S k y S u r v e y I I I : D e e p c

  • s

m

  • l
  • g

i c a l a p p l i c a t i

  • n
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SDSS3 data SDSS3 data

Panstarrs SDSS SDSS DR12 galaxy sample ~1.6 millions of galaxies

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Forward model becomes more complex Forward model becomes more complex

Cosmic growth of structures Cosmic expansion

(see Doogesh’ talk)

Implemented so far for (2)LPT: Non-linear density remapping:

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Forward model becomes more complex Forward model becomes more complex

Cosmic growth of structures Cosmic expansion

(see Doogesh’ talk)

Time

L

  • k

b a c k t i m e

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Forward model becomes more complex Forward model becomes more complex

Cosmic growth of structures Cosmic expansion

(see Doogesh’ talk)

Time

L

  • k

b a c k t i m e

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Some systematic cleaning… Some systematic cleaning…

11 foregrounds (here only 8)… still much less than Leistedt & Peiris (2014) but improving Star densities Sky fluxes DUST psfWidth ... ...

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Example fitted composite... Example fitted composite...

11 foregrounds (here only 8)… still much less than Leistedt & Peiris (2014) but improving Star densities Sky fluxes DUST psfWidth ... ...

Preliminary

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Inferred density of SDSS3 Inferred density of SDSS3

Ensemble density average Error estimate from ensemble variance Main galaxy sample limit (not included) LOWZ limit CMASS limit NGC SGC

Preliminary

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Sky density Sky density

Preliminary

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C

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c l u s i

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The Aquila consortium The Aquila consortium

https://aquila-consortium.org/

  • Founded in 2016
  • Gather people interested in working with each other on developing the Bayesian pipelines

and run analysis on data.

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Conclusion: great future Conclusion: great future

2M++ 2M++ SDSS SDSS CosmicFlows CosmicFlows LSST? LSST? BORG3+ BORG3+ Predictive cosmology Predictive cosmology Cosmological measurement Cosmological measurement

  • Velocity field (also VIRBIUS with F. Fuhrer)
  • X-ray cluster emission
  • Kinetic Sunyaev Zel’dovich
  • Rees-Sciama
  • Dark matter ?
  • Cosmic expansion (see Doogesh’s talk)
  • Power spectrum (and governing parameters)
  • Gaussianity tests of initial conditions
  • Direct probe of dynamics
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  • Cosmic expansion (see Doogesh’s talk)
  • Power spectrum (and governing parameters)
  • Gaussianity tests of initial conditions
  • Direct probe of dynamics

Conclusion: great future Conclusion: great future and challenges and challenges

2M++ 2M++ SDSS SDSS CosmicFlows CosmicFlows LSST? LSST? BORG3+ BORG3+ Predictive cosmology Predictive cosmology Cosmological measurement Cosmological measurement

  • Velocity field (also VIRBIUS with F. Fuhrer)
  • X-ray cluster emission
  • Kinetic Sunyaev Zel’dovich
  • Rees-Sciama
  • Dark matter ?

Galaxy formation: bias and likelihood Instrument modeling Galaxy formation: bias and likelihood Instrument modeling