With : Carlo Baccigalupi (SISSA) Radek Stompor (APC)

Yabebal Fantaye (SISSA)

Estimating the

TENSOR-TO-SCALAR RATIO

2SAAO, Cape Town08/23/10

Outline

CMB Review CMB polarization Polarization foregrounds Extracting CMB Polarization Parameter estimation Constraining r

3SAAO, Cape Town08/23/10

CMB Review I

➢ The cosmic microwave background is the The cosmic microwave background is the snapshot of the baby Universe when it was snapshot of the baby Universe when it was ~400,000 years old.~400,000 years old.

Simulated PLANCK 1 Year CMB Intensity Map

4SAAO, Cape Town08/23/10

CMB Review II

➢ Presence of quadrupolar temperature anisotropy at Presence of quadrupolar temperature anisotropy at decoupling yield a polarized CMB. CMB polarization decoupling yield a polarized CMB. CMB polarization carries complementary Information to that of the carries complementary Information to that of the CMB temperature.CMB temperature.

+Q U

Future and ongoing CMB Experiments

Satellite

PLANCK WMAP

resolution 5 arcminfrequency coverage: 9 (LFI and HFI)

resolution 14 arcminfrequency coverage: 5 (LFI) channels

Future and ongoing CMB Polarization Experiments

Charles Lawrence

7SAAO, Cape Town08/23/10

CMB POLARIZATION

08/23/10 SISSA student seminar

Stokes Q and U parameters

Origin of CMB polarization

E and B modes in real space

Polarization power spectrum

8SAAO, Cape Town08/23/10

Stokes Q and U parameters

I = |Ex|2 + |E

y|2

Q = |Ex|2 - |E

y|2

U = 2Re(ExE

y*)

V = 2Im(ExE

y*)

9SAAO, Cape Town08/23/10

Each point on the sphere has a Q or U value determined by the polarization at that point.

Stokes Q and U parameters

http://www.physics.princeton.edu/cosmology/capmap/polscience.html

10SAAO, Cape Town08/23/10

dσ Td

∝∣ε . ε '∣

The Origin of CMB Polarization

Blue shifted

Red shifted

Vertically polarized

Polarization of the CMB is inevitable if anisotropies exist at decoupling.

Only a quadrupolar anisotropy (as viewed by the electron) gives rise to polarization

Two sources:

● Density Perturbations at z=1000 lead to velocities that create “E-mode polarization” (no curl)

● Gravity waves: create “B-mode polarization” (curl)

The Origin of CMB Polarization II

Two sources:

● Density Perturbations at z=1000 lead to velocities that create “E-mode polarization” (no curl)

● Gravity waves: create “B-mode polarization” (curl)

The Origin of CMB Polarization II

GW

13SAAO, Cape Town08/23/10

E and B mode patterns II

Unchanged under parity flip

Sign reverses under parity flip

Q>0 U=0 Q<0 U=0

Q=0 U>0 Q=0 U<0

To disentangle the polarization created by the different perturbations we construct the E/ B field which has even and odd polarity. B-mode can only be generated by vector or tensor per.

14SAAO, Cape Town08/23/10

CMB B-mode polarization

Large scale Gaussian B-modes from primordial gravitational waves:

Inflation GW local quadrupole around the last scattering electron Thomson scattering E and B mode polarization

Non-Gaussian B-modes on small and large scales :

✔ expected signal from lensing of CMB✔ foregrounds, systematics, etc.

15SAAO, Cape Town08/23/10

CMB POWER SPECTRUM

• We expand T, E and B CMB modes in spherical harmonics.

• We can then form four possible CMB

power spectra TT, TE, EE and BB.

Tn

T 0

=∑l=1

∞

∑m=−l

l

a lmT Y lm n

16SAAO, Cape Town08/23/10

CMB polarisation spectra

• Have 4 possible spectra:: TT, TE, EE, BB.

• TB = EB = 0 by parity.by parity.

08/23/10 SISSA student seminar

GravitationalWaves

Reionisation

GravitationalLensing

17SAAO, Cape Town08/23/10

Tensor-to-scalar ratior = AT / AS

ATAS

http://space.mit.edu/~angelica/polarization.html

18SAAO, Cape Town08/23/10

B-mode power spectrum

The B-mode power spectrum from gravitational waves peaks around ℓ=100. On small and large scales the contribution from reionization and lensing dominates .

The amplitude of the B-mode power spectrum from gravitational wave is directly related to the energy scale of inflation and hence very ideal to probe the very early Universe.

19SAAO, Cape Town08/23/10

POLARIZATION FOREGROUNDS

Foreground levels

CMB vs. Foregrounds

20SAAO, Cape Town08/23/10

• The two dominant sources of polarization foregrounds are : Synchrotron, produced by cosmic-ray electrons orbiting in the total Galactic magnetic field, and Dust, absorption of starlight by aligned non-spherical dust grains.

• Free-free emission is unpolarized and spinning dust grains are expected to have polarization fractions of 1-2%.

• The signal from polarized radio sources is negligible.

Polarization foregrounds

21SAAO, Cape Town08/23/10

Polarization foregrounds

Page et al. 2007

r = 0.3, τ = 0.09

22SAAO, Cape Town08/23/10

SynchDustB-mode

Planck-NoiseEbex-Noise

Foregrounds at ℓ=100

CMB-B, Dust, Synch outside P06 and in EBEX region, and Planck + EBEX sensitivity

Ebex science proposal 2007

08/23/10 SISSA student seminar

23SAAO, Cape Town08/23/10

EXTRACTING CMB POLARIZATION

Foreground cleaning a.k.a. component separation

Power spectrum estimation

24SAAO, Cape Town08/23/10

CMB ANALYSIS PIPELINE FLOW

Data Collection Data Selection (cutting bad data) Data Filtering Data Calibration (relative calibration) Noise Estimation Map Estimation

Foreground Correction Power Spectrum Estimation Cosmological Parameter Estimation

25SAAO, Cape Town08/23/10

Simulation setup

Stivoli et al. 2010 - Suborbital experiments

1) Balloon-borne (EBEX like)fsky – 1%FWHM – 8‘F channels ( GHz ) - 150, 250, 410Noise levels (μK/3.5' pix) - 1.5, 4, 40

2) Ground-based (POLARBeaR like) fsky – 2.5%FWHM – 8‘F channels ( GHz ) – 90, 150, 220Noise levels (μK/3.5' pix) – 3, 3, 9 HighNoise levels (μK/3.5' pix) – 1, 1, 1 low

26SAAO, Cape Town08/23/10

Component separation I

Parameteric component separation (Stompor et al. 2009 ): solves the data model,

where A is the mixing matrix (contains the frequency scaling of the components) and n is noise

=A( ) + n

27SAAO, Cape Town08/23/10

Component separation II

For experiments with N channels, at most N parameters can be solved. In our case we have 3 channels and 4 parameters, CMB, dust and synchrotron amplitudes plus dust frequency scaling.

Assumptions : Basic – Self-contained FG separation. Synchrotron is assumed negligible (true for balloon experiment)

No Sync – Synchrotron component is not added in the simulation

28SAAO, Cape Town08/23/10

Ground and Balloon input spectra for the

150GHz channel

Stivoli et al. 2010

29SAAO, Cape Town08/23/10

Component separation III

Using ML parametric component separation Stivoli et al. concluded that

1) basic foreground + balloon, detection of r=0.04 is possible at 2-sigma

Stivoli et al. 2010

30SAAO, Cape Town08/23/10

2) Ground observation requires external information to reach similar precision to that of the balloon experiment.

Component separation III

Stivoli et al. 2010

31SAAO, Cape Town08/23/10

Component separation III

Given the estimate of the residual foreground, the total covariance matrix for the estimated power is written as

Where b(b') denotes the multipole bin number and Δ the residual foreground map

' ' ' '

32SAAO, Cape Town08/23/10

PARAMETER ESTIMATION

component separation

Power spectrum estimation

33SAAO, Cape Town08/23/10

Open problems

No one has yet done proper propagation of errors from foreground separation, power spectrum estimation to error on r.

Stivoli et al. result assumes that all parameters except r are perfectly known, which is not the case in reality.

Biases on the power spectrum by the presence of residual foregrounds needs to be properly accounted.

Covariances from instrument and foregrounds needs to be accurately propagated

34SAAO, Cape Town08/23/10

This work

Degeneracies of r with other parameters: we use the six WMAP parameters plus r, (Ωb,Ωm,θ,τ,ns,As, r), in our MCMC analysis. We choose CosmoMC to do this.

Residual foregrounds : we introduce a two parameter model to study the bias caused by the presence of the residual foreground

Covariance matrix : For now we assume uncorrelated instrumental noise + Cov from 100% correlated residual components.

We use a 9-dimensional Gaussian likelihood.