Primordial fluctuations 20

Isotropic 3K background.The most perfect blackbody we know

Dipole (3.4 mK).Our motion relative to CMB

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Boomerang

In search of acoustic peaks…

In search of acoustic peaks…

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What do we already know?

1. The usual stuff:

• Universe is flat.

• Since low matter content, there is a cosmological constant (ie. dark energy).

What do we already know?

Presence of harmonic oscillations: coherence of initial fluctuations

Strong evidence for either inflation (or a structureformation scenario that is rapid in time). Alternative scenarios for structure formation, such as cosmic defects, are ruled out.

The not so usual stuff:

In search of acoustic peaks…

MAP

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COBE

… and more peaks

The promised land…. (with Planck)

Hu & Dodelson (Annual Reviews 2002)

After Acoustic Peaks: Next Generation CMB

Asantha CoorayCaltech

Structure Evolution and Cosmology - October 31st, 2002

Cosmic Time Line

Cosmic Time Line

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AIGW ∝ Einflation2

What else can we do with CMB?

What else can we do with CMB?

I. Determine the energy scale of inflation

• CMB Polarization • The role of confusions: weak lensing• With confusions partly removed

CMB Polarization

• Polarization is described by Stokes-Q and -U• These are coordinate dependent • The two dimensional field is described by a gradient of a scalar (E) or curl of a pseudo-scale (B).

CMB Polarization

• Polarization is described by Stokes-Q and -U• These are coordinate dependent • The two dimensional field is described by a gradient of a scalar (E) or curl of a pseudo-scale (B).

Grad (or E) modes

Curl (or B) modes

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Temperature map: T(ˆ n )

Polarization map: P(ˆ n )=∇E +∇ ×B

(density fluctuations have nohandness, so no contributionto B-modes)

Kamionkowski et al. 1997; Seljak & Zaldarriaga 1997

Grad or E modes

Temperature and Polarization quadrupole

Keating et al. 2001

(Zaldarriaga 1997)

Grad or E modes: Reionization

Gravitational-waves

• Inflation predicts tensor perturbations due to primordial gravity waves

• Hard to detect with temperature information alone (contribute to large angle anisotropies, dominated by cosmic variance)

• Distinct signature in polarization (in terms of curl, or magnetic-like, modes)

Gravitational-waves

What else can we do with CMB?

I. Determine the energy scale of inflation

• CMB Polarization • The role of confusions: weak lensing• With confusions partly removed

Why confusions?

z ~ 1000 6-40? Structure formation today

• We are collecting photons from the last scattering surface

Gravitational EffectsScattering Effects

(via electrons)

Frequency shifts

Lensing deflectionsTime-delays

z ~ 1000 6-40? Structure formation today

• late-time universe: non-linear physics. Large scale structure modifiesCMB properties

Why confusions?

Gravitational Effects

• Geometric effect

Angular deflection of Photons

• Potential effect

Time delay of photons

(Seljak 1996; Zaldarriaga 2000; Hu 2000; Hu & Cooray 2000 and many more before)

Lensing and time-delay

Two effects combined lead to the Fermat potential

Gravitational Effects

• Geometric effect

Angular deflection of Photons

• Potential effect

Time delay of photons

(Seljak 1996; Zaldarriaga 2000; Hu 2000; Hu & Cooray 2000 and many more before)

Lensing and time-delay

Two effects combined lead to the Fermat potential

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T(θ ) ≡T(θ +δθ )

≈T(θ )+δθ •∇T(θ )+...

δθ ≡∇φ (Deflection angle)

Gravitational Effects

(Seljak 1996; Zaldarriaga 2000; Hu 2000; Hu & Cooray 2000 and many more before)

Lensing and time-delay

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T(θ ) ≡T(θ +δθ )

≈T(θ )+δθ •∇T(θ )+...

δθ ≡∇φ (Deflection angle)

Things needed

1. Large scale structuredeflections

2. CMB angular gradients

Cooray 2002

Contribution can be described as a result of effects in two regimes:Large scales: fluctuating CMB gradients modulated by large scale - slowly varying - mass fluctuations

Small scales: constant CMB gradient lensed by small scale mass fluctuations (smoothing and shifting of power )

Cooray 2002

Also in Polarization…

Lensing mixes Stokes-Q and U, or alternatively, between E and B.

(Seljak & Zaldarriaga 1998)

Curl modes: Gravitational-waves and lensing

Lensing vs. Gravitational-Waves: Which dominates?

After Planck???

Sensitivity less than 1/50th Planck with same beam…Lensing contribution detect with S/N~many hundreds.

Temperature field

Weak Lensing in CMB

Hu 2002

Temperature field Lensed temperature field

Weak Lensing in CMB

Hu 2002

Quadratic Statistics as a way to reconstruct lensing deflections

Reconstruction algorithm (basics) Lensing effect is on the second order - has to be a quadratic

statistic

CMB maps are noise dominated - has to be able to understand noise properties easily and be able to extract most information on lensing

Squared Temperature-Squared Temperature Power Spectrum

Hu 2001Hu & OkamatoCooray & Kesden 2002

Input deflection (mass) field Constructed deflection map with 1.5 arcmin beam and 27 arcmin noise

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μK

CMB as a weak lensing experiment

(Other suggestions: temperature gradientsSeljak & Zaldarriaga; Bernardeau et al.)

Hu 2001

• Detection of lensing potential power spectrum with Planck

Seljak & Zaldarriga 2000; Hu 2001; Cooray & Kesden 2002

Quadratic Statistics as a way to reconstruct lensing deflections

Cooray 2002

Lensing convergence

CMB as a weak lensing experiment

Z~1000

Z~1

Cooray 2002

Lensing convergence

CMB as a weak lensing experiment

Z~1000

Z~1

Why do this?

1. Source redshift is known (recombination)

2. Linear power spectrum -(cosmology)

3. Test evolution

4. Get this for free (no need for a CMB version of LSST)

Cooray 2002

Hu 2002

Lensing convergence

CMB as a weak lensing experiment

Z~1000

Z~1

Improvements to Parameters

CMB lensing Polarization

Lensing Extraction

Cooray & Kesden 2002

As a function of beamwidth with sensitivity of 1 microK/sec1/2

Gaussian noise

Additional non-Gaussian

Extract with a noisecontribution below anorder of magnitude ofthe signal

(Kesden et al. 2002;Knox & Song 2002)

Curl: Gravitational-Waves

With CMB temp. data cleanedFor lensing

Curl: Gravitational-Waves

With CMB lensing reconstruction -> Reasonable S/Ndetection of gravitational wave B-modes (unconfused !!!)

Post Planck mission (Planck noise/50, FWHM/3)

Kesden, Cooray & Kamionkowski 2002; also, Knox & Song 2002

Post-LISA mission(already a white paper to NASA SEU: GREAT by Cornish et al. Confusing backgrounds there is a separate issue)

Kesden, Cooray & Kamionkowski 2002

CMB polarization can be used to detect gravitational-waves

Lensing of scalar modes confuses the gravitational-wavesignal

The lensing effect can be separated in a model-independent manner using the CMB temperature data alone

Kesden, Cooray & Kamionkowski 2002

CMB polarization can be used to detect gravity-waves

Lensing of scalar modes confuses the gravity-wavesignal

The lensing effect can be separated in a model-independent manner using the CMB temperature data alone

Proposal: If one is to detect gravitationalwaves, also make a high resolution map of the temperature towards the area surveyedin polarization

Thermal Sunyaev-Zel’dovich Effect

This is Real! This is not, but we’ll get there….Observations: Carlstrom et al. Simulations: Pen et al.

• The statistics in a wide-field SZ map? • How to recover SZ from CMB?

Frequency Separation

Scattering moves photons from low frequencies (RJ part of the frequency spectrum) to high frequencies (Wien regime)

In the language of Sunyaev-Zel’dovich (1980):

Frequency shift the CMB blackbody and the difference (wrt to CMB)

Frequency Separation

Back to basics: how can we separate SZ from CMB?

In the language of Sunyaev-Zel’dovich (1980):

Frequency shift the CMB blackbody and the difference (wrt to CMB)

use frequency dependence of the SZ effect relative to CMB

Frequency Separation

decrement

increment

SZ null ~ 217 GHz

Back to basics: how can we separate SZ from CMB?

use frequency dependence of the SZ effect relative to CMB

combine experiments + known properties of foregrounds

Frequency Separation

Separation of SZ from CMB and rest in upcoming/present data

With Planck sensitivity:

Input SZ SZ+CMB+Foregrounds Recovered SZ

What can we do withthe recovered SZ map?Cooray, Hu & Tegmark 2000

(In real life, this is what we observe)

Can we measure the SZ power spectrum?

one sigma detection limits for SZ or SZ-like effect.

Thermal Sunyaev-Zel’dovich Effect

Cooray, Hu & Tegmark 2000; Foreground separations in Tegmark et al. 1999; Bouchet & Gispert 1999; Knox 1999;

Results from recent SZ related data

A2163:LaRoque et al. 2002

Thermal SZ

kinetic SZ

Novel Application: Measure CMB temperature at high redshift

Results from recent SZ related data

A2163:LaRoque et al. 2002 Battistelli et al. 2002(MITO Collaboration)

Thermal SZ

kinetic SZ

Novel Application: Measure CMB temperature at high redshift

Results from recent SZ related data

CN molecules

SZ clusters

Coma A2163

Constrain T_CMB(z)=T_0(1+z)

Battistelli et al. 2002; astro-ph/0208027

Can we measure the SZ power spectrum?

one sigma detection limits for SZ or SZ-like effect.

Thermal Sunyaev-Zel’dovich Effect

Cooray, Hu & Tegmark 2000; Foreground separations in Tegmark et al. 1999; Bouchet & Gispert 1999; Knox 1999;

How to describe the SZ contribution due to large scale structure?

Halo Approach to Large Scale StructureTowards a better analytical model:

Dark matter halo model for clustering:

Complex View Simplified View

Review article to appear in Physics Reports (Cooray & Sheth)

Halo Approach to Large Scale Structure

Basic idea:1. All dark matter in halos

2. Correlation functions canbe described through correlations within and between halos

3. Ingredients: halo profile

(NFW or variants) Mass function (Press-Schechter or variants) Halo bias model

Two point function

2-halo

1-halo

Dark matter halo model for clustering

Neyman & Scott 1952;Peebles 1974; Scherrer & Bertschinger 1991; Seljak 2000; Ma & Fry 2000; Scoccimarro et al 2000; Cooray, Hu, Miralda-Escudé 2000;

Dark matter power spectrum

Gas Profile

Sigurdson & Cooray 2002; data from Santa Barbara Comparison Project

Dark matter power spectrum

Temperature Profile

Sigurdson & Cooray 2002; data from Santa Barbara Comparison Project

Temperature Profile

Loken et al. 2002

Dark matter power spectrum

Self-similar solution

Sigurdson & Cooray 2002; data from various authors

Temperature-Mass Relation

Extensions to SZ: Pressure power spectrum

SZ line of sight projection of pressure power spectrum

Note: Poisson or single-haloterm dominates the SZ powerspectrum.

Why?

SZ effect:

Pressure power spect. is sensitive to halos with high temperature electrons. additional mass weighing compared to the dark matter power spectrum Poisson term boosted relative to the halo correlations

SZ Power Spectrum under thehalo model

Te ∝ M23

Results from recent SZ related data

Sigma_8=0.9

Sigma_8=1.1

Non-Gaussian errors: Cooray 2001

Results from recent SZ related data

Sigurdson, Cooray & Kamionkowski 2002

Is sigma_8 too high?

Currently preferred~0.7 to 0.8

Results from recent SZ related data

Sigurdson, Cooray & Kamionkowski 2002

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Not dominated by Point Sources

Results from recent SZ related data

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ClPoint−Source=5×10−17 APS

1.0⎛ ⎝

⎞ ⎠

Future CMB

There is more to CMB than just acoustic peaks

Full talk and details at http://www.its.caltech.edu/~asante

And why do we want to do this?

• Necessary to study inflation with polarization (e.g. remove lensing contribution)

• higher order effects can be used for further extraction and separation e.g., lensing studies with CMB