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An alternative probe of An alternative probe of CMB isotropy & foregroundsCMB isotropy & foregrounds

Miguel QuartinMiguel QuartinInstituto de FísicaInstituto de Física

Univ. Fed. do Rio de JaneiroUniv. Fed. do Rio de Janeiro

3939oo Partículas e Campos – C. Jordão – Sep 2018 Partículas e Campos – C. Jordão – Sep 2018

In collaboration with Renan de Oliveira & Thiago Pereira + Alessio Notari, Pedro S. Ferreira

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Fundamental Properties of the CMBFundamental Properties of the CMB

The simplest (toy) models of inflation predict the most The simplest (toy) models of inflation predict the most important properties of the CMB:important properties of the CMB: GaussianityGaussianity: the primordial fluctuations are nearly : the primordial fluctuations are nearly

GaussianGaussian Statistical IsotropyStatistical Isotropy & & Statistical HomogeneityStatistical Homogeneity: the : the

fluctuations do not depend, in average, on position or on fluctuations do not depend, in average, on position or on any directionany direction These two properties imply that for any scalar X:These two properties imply that for any scalar X:

Or, in spherical harmonics space:Or, in spherical harmonics space:

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Cosmic Microwave BackgroundCosmic Microwave Background

The CMB is one of the best tools to test cosmological The CMB is one of the best tools to test cosmological isotropy (on early times)isotropy (on early times)

So far, no strong deviations from global isotropy & So far, no strong deviations from global isotropy & homogeneity have been measuredhomogeneity have been measured

It also tells us that the primordial (perturbative) It also tells us that the primordial (perturbative) anisotropies are anisotropies are GaussianGaussian to a very good degree to a very good degree

Our precision has reached a level where control of Our precision has reached a level where control of systematics must be done to high accuracysystematics must be done to high accuracy

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Planck Satellite (2009–2012)Planck Satellite (2009–2012)

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Combine to extract the black-body partCombine to extract the black-body part

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CMB Power SpectrumCMB Power Spectrum

Planck 2013

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CMB Power SpectrumCMB Power SpectrumPlanck 2015 - Polarization

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Spreading Spherical Harmonic Love (Spreading Spherical Harmonic Love (ℓℓ≤≤10)10)

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Earth Topography [sea = 0] Earth Topography [sea = 0] ((ℓℓ ≤≤ 2000) 2000)

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Earth Topography SpectrumEarth Topography Spectrum

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Gaussian Earth Topography MapGaussian Earth Topography Map

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CMB Present StatusCMB Present Status

After Planck good measurements of all modes of the → good measurements of all modes of the After Planck good measurements of all modes of the → good measurements of all modes of the power spectrum up to power spectrum up to ℓℓ ~ 1700 ~ 1700 for TT, TE & EE for TT, TE & EE + 40+ 40σσ measurements of lensing measurements of lensing With BICEP, Polarbear & others, also some measurements With BICEP, Polarbear & others, also some measurements

of the lensing-induced BBof the lensing-induced BB In the future, Simons Observatory & In the future, Simons Observatory & CMB Stage 4CMB Stage 4 power → good measurements of all modes of the power → good measurements of all modes of the

spectra measurements up to spectra measurements up to ℓℓ ~ 4000 ~ 4000

CMB has been a fantastic success story of early universe CMB has been a fantastic success story of early universe cosmology: Big Bang, isotropy & standard inflationcosmology: Big Bang, isotropy & standard inflation There are however some There are however some “anomalies”“anomalies” in the data in the data

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CMB AnomaliesCMB Anomalies Planck sees only the expected non-Gaussianities (ISW + Planck sees only the expected non-Gaussianities (ISW +

lensing)lensing) Planck has confirmed the WMAP anomaliesPlanck has confirmed the WMAP anomalies

Same large scale (low-Same large scale (low-ℓ)ℓ) anomalies WMAP was already → good measurements of all modes of the anomalies WMAP was already → good measurements of all modes of the limited by cosmic variance for limited by cosmic variance for ℓℓ < 600. < 600.

The statistical significance of these is The statistical significance of these is around 3around 3σσ.. anomalies in cosmology are often at 3anomalies in cosmology are often at 3σ sociological?→ good measurements of all modes of the σ sociological?→ good measurements of all modes of the

If primordial, they violate the basic hypothesis: initial If primordial, they violate the basic hypothesis: initial fluctuations are statistically isotropic and Gaussianfluctuations are statistically isotropic and Gaussian

ALL anomalies could be trivial ALL anomalies could be trivial a posterioria posteriori statisticsstatistics How do we test if they are not simple data flukes?How do we test if they are not simple data flukes?

Planck 2018 I, Overview Planck 2013 XXIII, Isotropy & Statistics

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CMB Anomalies (2)CMB Anomalies (2)

The anomalies present in large angular scales are The anomalies present in large angular scales are (according to Planck 2013)(according to Planck 2013) Quadrupole-octopole alignmentQuadrupole-octopole alignment The low varianceThe low variance Phase correctionsPhase corrections Hemispherical asymmetryHemispherical asymmetry Dipolar power modulationDipolar power modulation Generalized power modulationGeneralized power modulation Parity asymmetryParity asymmetry The Cold SpotThe Cold Spot

Planck 2013, XXIII 1303.5083

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CMB Anomalies (3)CMB Anomalies (3) There are 3 ways to test if anomalies have a meaningThere are 3 ways to test if anomalies have a meaning

Look at more dataLook at more data Difficult, as the CMB temperature measurements are Difficult, as the CMB temperature measurements are

already fundamentally limited by cosmic variancealready fundamentally limited by cosmic variance But one can look at polarization (EE, ET/TE, BB)But one can look at polarization (EE, ET/TE, BB)

Planck 2018 isotropy paper not out yet!Planck 2018 isotropy paper not out yet! Think of an astrophysical explanation systematic effects→ good measurements of all modes of the Think of an astrophysical explanation systematic effects→ good measurements of all modes of the

E.g.: properly remove the Doppler quadrupoleE.g.: properly remove the Doppler quadrupole Did not solve!Did not solve!

E.g.: properly account for Doppler + aberration couplingsE.g.: properly account for Doppler + aberration couplings Solved for high-Solved for high-ℓℓ

Use a Use a different tooldifferent tool for the analysis for the analysis (see this talk)(see this talk)

Notari & Quartin 1504.02076 (JCAP)

Notari & Quartin 1408.5792 (JCAP)

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Multipole VectorsMultipole Vectors

Multipole vectors are an alternative to using the regular Multipole vectors are an alternative to using the regular spherical harmonic expansion spherical harmonic expansion [Maxwell, 1891][Maxwell, 1891] Substitute complex coefficients by 2-vectors Substitute complex coefficients by 2-vectors

These are headless vectorsThese are headless vectors

For each For each ℓℓ 2→ good measurements of all modes of the 2→ good measurements of all modes of the ℓℓ + 1 d.o.f. + 1 d.o.f. The “+1” is The “+1” is λλℓℓ contains the power spectrum (C→ good measurements of all modes of the contains the power spectrum (C→ good measurements of all modes of the ℓℓ) info!) info!

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Multipole Vectors (2)Multipole Vectors (2)

The separation of the power-spectrum info in a separate The separation of the power-spectrum info in a separate coefficient is a great advantagecoefficient is a great advantage All statistics on the 2-vectors → good measurements of all modes of the All statistics on the 2-vectors → good measurements of all modes of the independent of the Cindependent of the Cℓℓ

And thus independent on cosmology!And thus independent on cosmology!

E.g.: for a statistically isotropic map the E.g.: for a statistically isotropic map the vvℓℓ should also be should also be isotropic!isotropic!

Previous papers in the literature only analysed them on Previous papers in the literature only analysed them on large-scales due to their computational complexitylarge-scales due to their computational complexity We developed a We developed a fast methodfast method that allows their computation that allows their computation

on all scales!on all scales!

Helling, Schupp & Tesileanu astro-ph/0603594 (PRD)Pinkwart & Schwartz 1803.07473

Copi, Huterer & Starkman astro-ph/0310511 (PRD)

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M.pole vector code comparisonM.pole vector code comparison Public MV codes used to rely on solving a very large Public MV codes used to rely on solving a very large

number of algebraic equations number of algebraic equations Our code relies on finding the Our code relies on finding the ℓ ℓ roots of a complex roots of a complex

polinomialpolinomial

Oliveira, Pereira & Quartin (in prep)

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Multipole Vectors (3)Multipole Vectors (3)

The first thing to test is whether in the CMB data the The first thing to test is whether in the CMB data the vectors are isotropically distributedvectors are isotropically distributed

In practice, the need for In practice, the need for masksmasks in CMB analysis (to block in CMB analysis (to block the galatic plane and point sources) will break the the galatic plane and point sources) will break the isotropyisotropy We need simulations to understand the statistics with We need simulations to understand the statistics with

masksmasks We made 2000 Monte Carlo simulations of the CMB We made 2000 Monte Carlo simulations of the CMB

assuming Gaussianity and isotropy and compared the assuming Gaussianity and isotropy and compared the results with Planck dataresults with Planck data

Oliveira, Pereira & Quartin (in prep)

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Simulated MVs without mask Simulated MVs without mask

MVs are isotropic for a isotropic & Gaussian CMBMVs are isotropic for a isotropic & Gaussian CMB

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Simulated MVs with mask Simulated MVs with mask

Masks break the isotropy of the MVsMasks break the isotropy of the MVs

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MVs histogram and MVs histogram and χχ22 (with mask) (with mask)

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MVs histogram and MVs histogram and χχ22 (no mask) (no mask)

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MVs histogram and MVs histogram and χχ22 (2) (2)

Consistent with Gaussian & Isotropic CMB!!!

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Finding Preferred DirectionsFinding Preferred Directions

Since the MVs are headless vectors, we cannot simply Since the MVs are headless vectors, we cannot simply take the cartesian mean of vectorstake the cartesian mean of vectors

One possibility is to use the One possibility is to use the Fréchet meanFréchet mean FF For a given For a given ℓ, ℓ, FFℓℓ is the headless vector that minimizes is the headless vector that minimizes

For a CMB map with For a CMB map with ℓℓmaxmax we have ℓ we have ℓmaxmax Fréchet vectors Fréchet vectors

Each Each FFℓℓ is a is a preferred directionpreferred direction for that for that ℓℓ

The distribution of The distribution of FFℓℓ should also be isotropic (apart should also be isotropic (apart from masks)from masks)

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Fréchet vectors ResultsFréchet vectors Results

The Fréchet vectors can pick-up the directions of The Fréchet vectors can pick-up the directions of physical effectsphysical effects

1 – cos(θ)

E.g.: a CMB map E.g.: a CMB map with a boost with a boost corresponding corresponding to to ββ = v/c = 0.1 = v/c = 0.1 The boost is at The boost is at

the north-pole the north-pole ((θθ = 0) = 0)

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Fréchet vectors Results (2)Fréchet vectors Results (2)

The bare MVs (The bare MVs (i.e.i.e. not the Fréchets) on the other hand do not the Fréchets) on the other hand do not indicate a preferred directionnot indicate a preferred direction

η = 1 – cos(θ)

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MV sensitivity to anisotropiesMV sensitivity to anisotropies

Planck noise is NOT isotropicPlanck noise is NOT isotropic At high ℓAt high ℓ, this makes the whole map anisotropic, this makes the whole map anisotropic

The MV at high ℓThe MV at high ℓ point to the anisotropic regions! point to the anisotropic regions!

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MV sensitivity to anisotropiesMV sensitivity to anisotropies

At high ℓAt high ℓ the whole map anisotropic the whole map anisotropic The MV at high ℓThe MV at high ℓ point to the anisotropic regions! point to the anisotropic regions!

NILC Fréchets for ℓNILC Fréchets for ℓ < 2500 < 2500

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MV sensitivity to anisotropiesMV sensitivity to anisotropies

At high ℓAt high ℓ the whole map anisotropic the whole map anisotropic The MV at high ℓThe MV at high ℓ point to the anisotropic regions! point to the anisotropic regions!

Commander Fréchets for ℓCommander Fréchets for ℓ < 2500 < 2500

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ConclusionsConclusions CMB anomalies new fundamental physics (or astrophys.)→ good measurements of all modes of the CMB anomalies new fundamental physics (or astrophys.)→ good measurements of all modes of the

But they may be simple But they may be simple a posterioria posteriori statistical flukes statistical flukes Lacking reasonable systematic explanations, we require new Lacking reasonable systematic explanations, we require new

data or new toolsdata or new tools Multipole vectors alternative decomposition of sphere→ good measurements of all modes of the Multipole vectors alternative decomposition of sphere→ good measurements of all modes of the

They are They are independent on the power spectrumindependent on the power spectrum, which carries , which carries most cosmological informationmost cosmological information

Allows Allows blind searchblind search (not (not a posterioria posteriori) of preferred directions) of preferred directions Planck CMB data MV statistics isotropic and Gaussian→ good measurements of all modes of the Planck CMB data MV statistics isotropic and Gaussian→ good measurements of all modes of the

MVs are sensitive to foregrounds useful in detecting them→ good measurements of all modes of the MVs are sensitive to foregrounds useful in detecting them→ good measurements of all modes of the

Obrigado!Oliveira, Pereira & Quartin (in prep)

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ExtraExtra

SlidesSlides

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MVs histogram and MVs histogram and χχ22

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Primordial CMB dipole? (2)Primordial CMB dipole? (2)

Aberration-couplings are in general NOT produced, unless Aberration-couplings are in general NOT produced, unless we fine-tune the radial profile of the grav potential (due to we fine-tune the radial profile of the grav potential (due to an induced dipolar lensing effect).an induced dipolar lensing effect). If the dipole is isocurvature, we also need to fine-tune If the dipole is isocurvature, we also need to fine-tune

the distance to the LSS!the distance to the LSS!

Roldan, Notari & Quartin 1603.02664 (JCAP)

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Future of Aberration: COREFuture of Aberration: CORE

Exploring cosmic origins with CORE 1704.05764

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Future of Aberration: comparisonFuture of Aberration: comparison

Exploring cosmic origins with CORE 1704.05764

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Quadrupole AnomaliesQuadrupole Anomalies

The The value of the quadrupolevalue of the quadrupole is a b it low compared to is a b it low compared to ΛΛCDM expected valueCDM expected value CC22(meas) (meas) ≈≈ 250 ( 250 (μμK)K)22 ; C ; C22(theory) = 1170 ((theory) = 1170 (μμK)K)22

Significance: < 2σSignificance: < 2σ The The quadrupole directionquadrupole direction is observed to be very close to is observed to be very close to

the octupole directionthe octupole direction There are 2 ways to define a multipole direction:There are 2 ways to define a multipole direction:

Multipole vectors Multipole vectors vvℓℓ ( (ℓℓ vectors for multipole vectors for multipole ℓℓ))

Max. “angular momentum” direction: Max. “angular momentum” direction: nnℓ ℓ (1 for each ℓ)(1 for each ℓ)

Significance: between 2 and 3σSignificance: between 2 and 3σ

Notari & Quartin 1504.02076 (JCAP)

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Quadrupole Anomalies (4)Quadrupole Anomalies (4) We computed the average correction “Q” for each We computed the average correction “Q” for each

Planck map (different combinations of the frequencies)Planck map (different combinations of the frequencies)

Notari & Quartin 1504.02076 (JCAP)