primordial fluctuations 20 isotropic 3k background. the most perfect blackbody we know dipole (3.4...
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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
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In search of acoustic peaks…
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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).
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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:
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In search of acoustic peaks…
MAP
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COBE
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… and more peaks
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The promised land…. (with Planck)
Hu & Dodelson (Annual Reviews 2002)
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After Acoustic Peaks: Next Generation CMB
Asantha CoorayCaltech
Structure Evolution and Cosmology - October 31st, 2002
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Cosmic Time Line
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Cosmic Time Line
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€
AIGW ∝ Einflation2
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What else can we do with CMB?
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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
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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).
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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
€
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
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Grad or E modes
Temperature and Polarization quadrupole
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Keating et al. 2001
(Zaldarriaga 1997)
Grad or E modes: Reionization
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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)
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Gravitational-waves
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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
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Why confusions?
z ~ 1000 6-40? Structure formation today
• We are collecting photons from the last scattering surface
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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?
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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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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
€
T(θ ) ≡T(θ +δθ )
≈T(θ )+δθ •∇T(θ )+...
δθ ≡∇φ (Deflection angle)
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Gravitational Effects
(Seljak 1996; Zaldarriaga 2000; Hu 2000; Hu & Cooray 2000 and many more before)
Lensing and time-delay
€
T(θ ) ≡T(θ +δθ )
≈T(θ )+δθ •∇T(θ )+...
δθ ≡∇φ (Deflection angle)
Things needed
1. Large scale structuredeflections
2. CMB angular gradients
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Cooray 2002
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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 )
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Cooray 2002
Also in Polarization…
Lensing mixes Stokes-Q and U, or alternatively, between E and B.
(Seljak & Zaldarriaga 1998)
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Curl modes: Gravitational-waves and lensing
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Lensing vs. Gravitational-Waves: Which dominates?
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After Planck???
Sensitivity less than 1/50th Planck with same beam…Lensing contribution detect with S/N~many hundreds.
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Temperature field
Weak Lensing in CMB
Hu 2002
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Temperature field Lensed temperature field
Weak Lensing in CMB
Hu 2002
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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
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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
€
μK
CMB as a weak lensing experiment
(Other suggestions: temperature gradientsSeljak & Zaldarriaga; Bernardeau et al.)
Hu 2001
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• 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
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Cooray 2002
Lensing convergence
CMB as a weak lensing experiment
Z~1000
Z~1
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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)
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Cooray 2002
Hu 2002
Lensing convergence
CMB as a weak lensing experiment
Z~1000
Z~1
Improvements to Parameters
CMB lensing Polarization
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Lensing Extraction
Cooray & Kesden 2002
As a function of beamwidth with sensitivity of 1 microK/sec1/2
Gaussian noise
Additional non-Gaussian
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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
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Curl: Gravitational-Waves
With CMB lensing reconstruction -> Reasonable S/Ndetection of gravitational wave B-modes (unconfused !!!)
Post Planck mission (Planck noise/50, FWHM/3)
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Kesden, Cooray & Kamionkowski 2002; also, Knox & Song 2002
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Post-LISA mission(already a white paper to NASA SEU: GREAT by Cornish et al. Confusing backgrounds there is a separate issue)
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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
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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
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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?
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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)
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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
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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
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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)
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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;
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Results from recent SZ related data
A2163:LaRoque et al. 2002
Thermal SZ
kinetic SZ
Novel Application: Measure CMB temperature at high redshift
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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
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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
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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?
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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)
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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;
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Dark matter power spectrum
Gas Profile
Sigurdson & Cooray 2002; data from Santa Barbara Comparison Project
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Dark matter power spectrum
Temperature Profile
Sigurdson & Cooray 2002; data from Santa Barbara Comparison Project
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Temperature Profile
Loken et al. 2002
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Dark matter power spectrum
Self-similar solution
Sigurdson & Cooray 2002; data from various authors
Temperature-Mass Relation
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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
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Results from recent SZ related data
Sigma_8=0.9
Sigma_8=1.1
Non-Gaussian errors: Cooray 2001
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Results from recent SZ related data
Sigurdson, Cooray & Kamionkowski 2002
Is sigma_8 too high?
Currently preferred~0.7 to 0.8
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Results from recent SZ related data
Sigurdson, Cooray & Kamionkowski 2002
|||||
Not dominated by Point Sources
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Results from recent SZ related data
€
ClPoint−Source=5×10−17 APS
1.0⎛ ⎝
⎞ ⎠
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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