Using cosmological surveys to map out the invisible (and the visible) matter

Yuuki Omori  (U.Chicago/KICP)

Credit: Aman Chokshi (2021 Winter Over)

Cosmic history

1

Cosmic microwave background

Cosmology

\Omega_{\Lambda}
\Omega_{\rm CDM}
\Omega_{\rm b}

Dark energy

Dark matter

Ordinary matter

(5%)

(26%)

(69%)

The goal of this talk is to describe how we map the distribution of invisible and visible matter

2

Weak gravitational lensing

Background light

Matter between

the light source and us

3

Weak gravitational lensing

Cosmic microwave background

(Undistored temperature map)

Cosmic microwave background

(Distorted temperature map)

4

Distant galaxies

Nearby massive

object

Undistorted background

galaxy image

Cosmic microwave background

(Undistored temperature map)

Cosmic microwave background

(Distorted temperature map)

4

Weak gravitational lensing

Nearby massive

object

Distorted background

galaxy image

Cosmic microwave background

(Undistored temperature map)

Cosmic microwave background

(Distorted temperature map)

4

Weak gravitational lensing

Distant galaxies

Reconstruction approach

CMB lensing 

3D gravitational potential

\Psi (\chi\hat{n},\chi)
\Psi

5

Reconstruction approach

CMB lensing 

3D gravitational potential

\phi(\hat{n})=-2\int d\chi \frac{\chi_{\rm CMB}-\chi}{\chi\chi_{\rm CMB}} \Psi (\chi\hat{n},\chi)

2D potential

\Psi (\chi\hat{n},\chi)
\Psi
\phi

5

Reconstruction approach

CMB lensing 

3D gravitational potential

\phi(\hat{n})=-2\int d\chi \frac{\chi_{\rm CMB}-\chi}{\chi\chi_{\rm CMB}} \Psi (\chi\hat{n},\chi)

2D potential

\Psi (\chi\hat{n},\chi)
\Psi
\phi
\vec{\alpha}=\vec{\nabla}\phi(\hat{n})

Deflection

5

{\kappa}=\vec{\nabla}^{2}\phi(\hat{n})

Convergence

Reconstruction approach

CMB lensing 

T^{d}(\vec{n})=T^{u}(\vec{n}+\vec{\alpha})\\
=T^{u}(\vec{n})+\vec{\nabla} T^{u}(\vec{n}) \vec{\nabla}\phi(\hat{n})\\
\langle T^{u}_{\ell m} (T^{u}_{\ell' m'})^{*} \rangle_{\ell\neq\ell',m\neq m'}=0
\langle T^{d}_{\ell m} (T^{d}_{\ell' m'})^{*} \rangle_{\ell\neq\ell',m\neq m'}=\sum_{LM}(-1)^{M}\begin{pmatrix} \ell & \ell' & L\\ m & m' & M \end{pmatrix}W^{\phi}_{\ell L \ell'}\phi_{LM}

Two independent modes become correlated through the lensing potential

\vec{\alpha}=\vec{\nabla}\phi(\hat{n})

6

{\rm Convergence}\ (\kappa=-\vec{\nabla}^{2}\phi)
{\rm Lensing\ potential}\ (\phi)
{\rm Deflection}\ (\vec{\alpha}=\vec{\nabla}\phi)
{\rm Direction\ with\ more\ mass}
{\rm Direction\ with\ less\ mass}

SPT-3G lensing map

(see also: Omori2017, Omori2023)

7

Reconstruction approach

CMB lensing - challenges (foregrounds)

8

SPT-3G temperature map

Reconstruction approach

CMB lensing - challenges (foregrounds)

SPT-3G temperature map

SPT-CLJ0234-5831

8

Reconstruction approach

CMB lensing - challenges (foregrounds)

SPT-3G temperature map

SPT-CLJ0234-5831

8

Reconstruction approach

CMB lensing - challenges (foregrounds)

\langle T^{u}_{\ell m} (T^{u}_{\ell' m'})^{*} \rangle_{\ell\neq\ell',m\neq m}=0

SPT-3G temperature map

PKS 2356-61

SPT-CLJ0234-5831

8

Reconstruction approach

CMB lensing - challenges (foregrounds)

Agora simulation (Omori 2022)

Multi-Dark Planck 2

N-body simulation 

(Klypin et al. 2017)

9

tSZ

kSZ

CIB

radio

Reconstruction approach

Galaxy lensing 

\gamma(\hat{n})=\gamma_{1}(\hat{n})+i\gamma_{2}(\hat{n})=\sum_{\rm \ell m} \gamma_{\ell m}\ _{2}Y_{\ell m}
\gamma_{\ell m}=\gamma_{{\rm E},\ell m} + i \gamma_{{\rm B},\ell m}
= -\sqrt{\frac{(\ell+2)(\ell-1)}{\ell(\ell+1)}}(\kappa_{{\rm E},\ell m}+\kappa_{{\rm B},\ell m})

10

(see Tianao & Emma's paper)

+\gamma_{\rm E}
-\gamma_{\rm E}
+\gamma_{\rm B}
-\gamma_{\rm B}

Reconstruction approach

Galaxy lensing map

11

Jeffery2021

Map of        from the

Dark Energy Survey 

\kappa_{\rm E}

Reconstruction approach

red border
red border
red border

DES galaxy lensing

map (overlay)

 SPT-3G CMB  lensing map (base)

Lensing map comparison

12

(see also: Omori2018, Chang2023)

Forward modeling approach

Increasing number people have started to work on forward modeling approach due to increased computational power.

\Omega_{\rm CDM},\ \Omega_{\rm b},\ \Omega_{\Lambda}\ {\rm etc.}

Gravitational/hydro-dynamical simulation

Ray-tracing

(light-propagation)

Predicted observed  fields

Comparison with data

Computationally expensive

Repeat until predicted maps look like data

Approximate methods

13

Forward modeling approach

15

Preliminary work

Galaxy lensing forward modeling (fixed seed)

Forward modeling approach

Galaxy lensing forward modeling (varying seed)

16

Preliminary work

(Millea et al. 2021)

CMB lensing forward modeling

Forward modeling approach

14

Total matter

\Omega_{\Lambda}
\Omega_{\rm CDM}
\Omega_{\rm b}

Dark energy

Dark matter

Ordinary matter

(5%)

(26%)

(69%)

17

Forward modeling approach

Challenges (Impact of astrophysical effects)

Dark matter

Ordinary matter (gas/stars)

18

Forward modeling approach

Challenges (Impact of astrophysical effects)

Illustris

Astrid

Simba

19

Forward modeling approach

Challenges (Impact of astrophysical effects)

Incoming data

Simons Observatory/CMB-S4

South Pole Observatory/CMB-S4

Euclid

Rubin/LSST

20

Summary

21

  • A map of the total matter distribution can be made using the weak gravitational lensing effect.
     
  • Two different types of backlight can be used: cosmic microwave background and distant galaxies.
     
  • Both approaches have their own challenges.
     
  • Forward modeling approaches are starting to gain more attention due to increased computational capabilities and efficiency.
     
  • Currently at an exciting time -- we already have good data, but the quality will become orders of magnitude better soon.