Cosmological inference from self-consistent Bayesian forward - - PowerPoint PPT Presentation

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Cosmological inference from self-consistent Bayesian forward - - PowerPoint PPT Presentation

Aug 27, 2022 42 likes •238 views

Cosmological inference from self-consistent Bayesian forward modelling of deep galaxy redshift surveys Doogesh Kodi Ramanah Guilhem Lavaux Jens Jasche Ben Wandelt Institut dAstrophysique de Paris Statistical challenges for large-scale

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SLIDE 1

Cosmological inference from self-consistent Bayesian forward modelling of deep galaxy redshift surveys

Doogesh Kodi Ramanah

Guilhem Lavaux Jens Jasche Ben Wandelt Institut d’Astrophysique de Paris

Statistical challenges for large-scale structure in the era of LSST, Oxford, 2018

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Cosmological data challenges

Noisy large-scale structure data

  • Incomplete noisy sky with systematic efgects (masks, complex noise models, ...)
  • Transformation: physical (comoving) space observational space

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 1

Cosmology encoded in expansion & global geometry (Alcock-Paczyński efgect)

signal reconstruction

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SLIDE 3

Cosmological data challenges

Noisy large-scale structure data

  • Incomplete noisy sky with systematic efgects (masks, complex noise models, ...)
  • Transformation: physical (comoving) space observational space

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 1

ALTAIR (ALcock-Paczyński consTrAIned Reconstruction)

  • Liberate cosmology → Cosmological parameter inference via the Alcock-Paczyński (AP) test
  • Also jointly infer underlying 3D power spectrum + more realistic (non-linear) bias model

(DKR, Lavaux & Wandelt 2018, in prep.)

HADES BORG ALTAIR AQUILA Consortium

Credit: Assassin’s Creed (Ubisoft)

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SLIDE 4

Alcock-Paczyński Test

Coordinate Transformation

Redshift space Comoving space SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 2

  • Test of the expansion & geometry of the Universe
  • No dependence on evolution of galaxies but only on geometry of Universe
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SLIDE 5

Alcock-Paczyński Test

Redshift space Comoving space

  • Test of the expansion & geometry of the Universe
  • No dependence on evolution of galaxies but only on geometry of Universe
  • Distortions due to assumption
  • f incorrect cosmological

parameters

  • Structure:

Spherical → Ellipsoidal

  • Statistical distribution:

Isotropic → Anisotropic

Coordinate Transformation

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 2

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SLIDE 6

Visualising cosmic expansion

[Standard ΛCDM]

  • SCLSS 2018, Oxford

Cosmological inference from Bayesian forward modelling of galaxy surveys 3

Initial conditions

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SLIDE 7

Visualising cosmic expansion

[Standard ΛCDM]

  • SCLSS 2018, Oxford

Cosmological inference from Bayesian forward modelling of galaxy surveys 3

Final (LPT) density fjeld

Comoving space

Initial conditions

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SLIDE 8

Visualising cosmic expansion

[Standard ΛCDM]

  • SCLSS 2018, Oxford

Cosmological inference from Bayesian forward modelling of galaxy surveys 3

Final (LPT+AP) density fjeld

Redshift space

Initial conditions

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SLIDE 9

Visualising cosmic expansion

[Einstein-de Sitter Universe]

  • SCLSS 2018, Oxford

Cosmological inference from Bayesian forward modelling of galaxy surveys 3

Final (LPT+AP) density fjeld Initial conditions

Redshift space

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ALTAIR reconstruction scheme

Data model:

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 4

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ALTAIR reconstruction scheme

Data model:

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 4

  • Redshift space representation

allows comparison with data via likelihood

comoving grid redshift grid

coordinate transformation + trilinear interpolation

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ALTAIR reconstruction scheme

Data model:

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 4

  • Redshift space representation

allows comparison with data via likelihood

comoving grid redshift grid

coordinate transformation + trilinear interpolation Transforms Gaussian initial conditions into a non-linearly evolved fjeld

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SLIDE 13

Validation on mock catalogues (A) - 2M++

2M++ galaxy compilation :

  • Superset of {2MASS, SDSS-DR7, 6dFGRS-DR3} redshift surveys
  • Greater depth & higher sampling than IRAS survey
  • Sub-divided into 2 K-bands
  • Anisotropic selection and strong galaxy clustering

(Lavaux & Hudson 2011)

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 5

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SLIDE 14

Validation on mock catalogues (A) - 2M++

2M++ galaxy compilation :

  • Superset of {2MASS, SDSS-DR7, 6dFGRS-DR3} redshift surveys
  • Greater depth & higher sampling than IRAS survey
  • Sub-divided into 2 K-bands
  • Anisotropic selection and strong galaxy clustering

(Lavaux & Hudson 2011)

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 5

Grid with 32³ voxels 1200 Mpc side length

  • Tested on low-resolution mock data
  • Forward model: LPT + AP
  • ~ Linear expansion regime
  • Broad posterior for Ωm

Simulation box

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SLIDE 15

Validation on mock catalogues (B) - SDSSIII

  • Forward model: LPT + AP
  • Highly structured survey geometry & selection

efgects

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 6

Sky completeness Grid with 128³ voxels 4000 Mpc side length Simulation box

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Validation on mock catalogues (B) - SDSSIII

  • Forward model: LPT + AP
  • Probing higher redshift range; AP distortion due

to cosmic expansion is much more informative

  • Tight constraints on Ωm

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 6

Sky completeness Grid with 128³ voxels 4000 Mpc side length Simulation box

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SLIDE 17

Ensemble mean & error maps

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 7

Slice through 3D density fjeld

Final density fjeld Initial density fjeld

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Current & future work

Current project:

  • Implemented forward model for AP distortion and cosmological parameter sampler
  • Tested on low-resolution mock (2M++, SDSS-III) data
  • Chain forward models: LPT + AP
  • Upgrade forward model to 2LPT and jointly infer mean density of tracers & bias also
  • Assess impact of redshift space distortions (RSDs) on cosmological constraints

(DKR, Lavaux & Wandelt 2018c, in prep.)

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 8

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SLIDE 19

Current & future work

Current project:

  • Implemented forward model for AP distortion and cosmological parameter sampler
  • Tested on low-resolution mock (2M++, SDSS-III) data
  • Chain forward models: LPT + AP
  • Upgrade forward model to 2LPT and jointly infer mean density of tracers & bias also
  • Assess impact of redshift space distortions (RSDs) on cosmological constraints

Future work:

  • Encode power spectrum inference in the block sampling scheme
  • Account for RSDs in the data model
  • Showcase application of ALTAIR on real data sets (e.g. SDSS-III):

→ Joint inference of 3D density fjeld, underlying power spectrum & cosmological parameters

(DKR, Lavaux & Wandelt 2018c, in prep.)

SCLSS 2018, Oxford Cosmological inference from Bayesian forward modelling of galaxy surveys 8

Relevant for current & next-generation galaxy redshift surveys (Euclid, LSST, ...)

Follow-up project