A Bayesian approach Florent Leclercq Institut dAstrophysique de - - PowerPoint PPT Presentation

Florent Leclercq

How is the cosmic web woven? – A Bayesian approach

Florent Leclercq

Institut d’Astrophysique de Paris Institut Lagrange de Paris École polytechnique ParisTech

May 14th, 2015

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

1

In collaboration with: Jens Jasche (Excellence Cluster Universe, Garching), Benjamin Wandelt (IAP/U. Illinois), Matías Zaldarriaga (IAS Princeton)

Florent Leclercq

BORG at work – chronocosmography

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

2

Observations Final conditions Initial conditions

Jasche, FL & Wandelt 2015, arXiv:1409.6308

Florent Leclercq

Bayesian chronocosmography from SDSS DR7

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

3

One sample

Jasche, FL & Wandelt 2015, arXiv:1409.6308

Florent Leclercq

Bayesian chronocosmography from SDSS DR7

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

4

Posterior mean

Jasche, FL & Wandelt 2015, arXiv:1409.6308

Florent Leclercq

Uncertainty quantification

• Each sample: a
• In Bayesian large-scale structure inference, the variation between

samples

that results from

having, e.g.

• incomplete observations (mask, finite volume and number of galaxies,

selection effects)

• an imperfect experiment (noise, biases, photometric redshifts…)
• only one Universe (a more precise version of “cosmic variance”)

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

5

Florent Leclercq

Uncertainty quantification

• Uncertainty quantification is

!

• Can we

to structure type classification?

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

6

Florent Leclercq

COLA: COmoving Lagrangian Acceleration

• Write the displacement vector as:
• Time-stepping (omitted constants and Hubble expansion):

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

7

Standard: Modified:

Tassev & Zaldarriaga 2012, arXiv:1203.5785 Tassev, Zaldarriaga & Einsenstein 2013, arXiv:1301.0322 20 Mpc/h

Florent Leclercq

Non-linear filtering of BORG samples

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

8 FL, Jasche, Sutter, Hamaus & Wandelt 2015, arXiv:1410.0355 = Fast constrained simulations of the Nearby Universe

Florent Leclercq

Non-linear filtering of BORG samples

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

9 FL, Jasche, Sutter, Hamaus & Wandelt 2015, arXiv:1410.0355

The usable for cosmology scales like k3!

= Fast constrained simulations of the Nearby Universe

Florent Leclercq

Hahn et al. 2007, arXiv:astro-ph/0610280 see also:

• Extensions:

Forero-Romero et al. 2009, arXiv:0809.4135 Hoffman et al. 2012, arXiv:1201.3367

• Similar web classifiers:

DIVA, Lavaux & Wandelt 2010, arXiv:0906.4101 ORIGAMI, Falck, Neyrinck & Szalay 2012, arXiv:1201.2353

Tidal shear analysis

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

10

• : eigenvalues of the tidal field tensor, the Hessian of

the gravitational potential:

• Voids:
• Sheets:
• Filaments:
• Clusters:

Florent Leclercq

Dynamic structures inferred by BORG

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

11

Final conditions

FL, Jasche & Wandelt 2015, arXiv:1502.02690

Florent Leclercq

Dynamic structures inferred by BORG

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

12

Initial conditions

FL, Jasche & Wandelt 2015, arXiv:1502.02690

Florent Leclercq

Kullback-Leibler divergence posterior/prior

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

13

Initial conditions Final conditions

in Sh

FL, Jasche & Wandelt 2015, arXiv:1502.02690

Florent Leclercq

A decision rule for structure classification

• Space of “input features”:
• Space of “actions”:
• A problem of

:

• ne should take the action that maximizes the expected utility
• How to write down the gain functions?

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

14 FL, Jasche & Wandelt 2015, arXiv:1503.00730

Florent Leclercq

• One proposal:
• Without data, the expected utility is
• With , it’s a fair game always play “speculative

map” of the LSS

• Values represent an aversion for risk increasingly

“conservative maps” of the LSS

Gambling with the Universe

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

15 “Winning” “Loosing” “Not playing” “Playing the game” “Not playing the game” FL, Jasche & Wandelt 2015, arXiv:1503.00730

Florent Leclercq

Playing the game…

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

16

Final conditions

FL, Jasche & Wandelt 2015, arXiv:1503.00730 voids sheets filaments clusters undecided

Florent Leclercq

Playing the game…

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

17

Initial conditions

FL, Jasche & Wandelt 2015, arXiv:1503.00730 voids sheets filaments clusters undecided

Florent Leclercq

Summary & Conclusions

• (More)
• Uncertainty quantification (noise, survey geometry, selection effects and

biases)

• A non-linear and non-Gaussian inference with improving techniques
• (More)
• Simultaneous analysis of the morphology and formation history of the

cosmic web

• Characterization of dynamic structures underlying galaxies
• A new framework for problems of classification in the presence of

uncertainty

May 14th, 2015 How is the cosmic web woven? – A Bayesian approach

18