An Uncooperative Universe: large scale anomalies in the CMB Glenn Starkman Institute for the Science of Origins CERCA, and Department of Physics Case Western Reserve University Cosmology on Safari 2017 Let your model guide you, but you can’t let your model boss you around. Don’t just ask the questions your model tells you are interesting, b/c you might get interesting answers to uninteresting questions. That is what forces you to think harder about your model. Craig Copi, Dragan Huterer & Dominik Schwarz Francesc Ferrer, Amanda Yoho S. Aiola, A. Kosowsky L. Knox, Marcio O’Dwyer; \ “photo”: ESA/ Planck Image: NASA/WMAP

WMAP NASA/WMAP Science team Galactic foreground removed by taking linear combination of bands. NASA/WMAP Science team

Planck NASA/WMAP Science team Galactic foreground removed by taking linear combination of 5 bands. NASA/WMAP Science team

Angular Power Spectrum Cl = (2l +1)-1m |al m|2 T = l mal m Yl m(,) Standard model for the origin of fluctuations (inflation): al m are independent (nearly?) Gaussian random variables, with < al m a*l’ m’> = Cl l l ‘mm’ Sky is statistically isotropic and Gaussian random, (almost) ALL interesting information is contained in Cl

Angular Power Spectrum NASA/WMAP Science team Cl = (2l +1)-1m |al m|2 T = l mal m Yl m(,) 6 parameter fit to >>6 points Planck 2013 Paper I.

Great experimental accomplishment Remarkable agreement with theory, especially for the statistics that the theory prefers BUT ! or but? Not talk about: cold spot (yesterday), SH (not anomalous), …

Is there anything interesting left to learn about the Universe on large scales?

Outline Alignments at low-l : The low-l / large-angle problem: The failure of statistical isotropy. The low-l / large-angle problem: The vanishing of C() And hemispheres, parity, first peak (, …?) Not talk about: cold spot (yesterday), SH (not anomalous), … Troubles in cosmological paradise? Can we tell? Even without a model?

“The Low-l Anomaly” Original Motivation:

Beyond Cl: Searches for Departures from Gaussianity/Statistical Isotropy angular momentum dispersion axes (da Oliveira-Costa, et al.) Genus curves (Park) Spherical Mexican-hat wavelets (Vielva et al.) Bispectrum (Souradeep et al.) North-South asymmetries (Eriksen et al., Hansen et al.) dipolar modulations Cold hot spots, hot cold spots (Larson and Wandelt) Land & Magueijo scalars/vectors even/odd Cl anomaly your favourite technique/anomaly that I missed multipole vectors (Copi, Huterer & GDS; Schwarz, SCH; CHSS; also Weeks; Seljak and Slosar; Dennis)

Alignments …

Multipole Vectors Advantages: 1) û (1,1) is a vector, A(1) is a scalar Q: What are the directions associated with the l th multipole: Tl ()  m al mYl m ()  Dipole (l =1) : m a1mY1m () = A(1) (ûx(1,1), ûy(1,1), ûz(1,1)) (sin cos, sin sin, cos) Advantages: 1) û (1,1) is a vector, A(1) is a scalar 2) Only A(1) depends on C1

Multipole Vectors {{al m, m=- l,…, l }, l =(0,1,)2,…}  General l, write: m al mYl m ()  A (l) (û (l,1)ê)…(û (l, l) ê ) - all traces] {{al m, m=- l,…, l }, l =(0,1,)2,…}  {A(l) ,{û (l,i),i =1,… l }, l = (0,1,)2,…} Advantages: 1) û(l,i) are vectors, A(l) is a scalar 2) Only A(l) depends on Cl

Maxwell Multipole Vectors m al mYl m ()  A(l) (û (l,1))… (û (l,l) )r -1] r=1 manifestly symmetric AND trace free: 2 (1/r)  (r) J.C. Maxwell, A Treatise on Electricity and Magnetism, v.1, 1873 (1st ed.)

Area Vectors Notice: Suggests defining: Quadrupole has 2 vectors, i.e. quadrupole is a plane Octopole has 3 vectors, i.e. octopole is 3 planes Suggests defining: w(l,i,j)  (û (l,i) x û (l,j)) “area vectors” Carry some, but not all, of the information Relation to ni: w(2,2,2) || n2 octopole is perfectly planar if w(3,1,2) || w(3,2,3) || w(3,3,1) and then: n3 || w(3,I,j) A. de Oliveira-Costa, M. Tegmark, M. Zaldarriaga, A. Hamilton. Phys.Rev.D69:063516,2004

l=2&3 Area Vectors ecliptic SGP l=3 normal l=3 normal equinox dipole l=3 normal ecliptic Quadrupole–octopole axis IS the “Axis of Evil” of Land and Maguejio SGP

Quadrupole plane & 3 octopole planes are: aligned perpendicular to the ecliptic normal to the dipole

Area vectors tell about the orientations of the multipole planes. Can still rotate the aligned planes about their common axis.

l=2&3 : The Map Note: ecliptic, N-S asymmetry

(WMAP3) Alignment “probabilities” p-value of the quadrupole & octopole planes being so aligned: (0.1-0.6)% Conditional p-value of these planes being so perpendicular to the ecliptic (solar system): (0.2-1.7)% Conditional p-value of aligned planes perpendicular to the ecliptic pointing at the dipole/equinox: few% Conditional p-value of aligned planes perpendicular to the ecliptic pointing at the dipole/equinox, rotated to have ecliptic separate high and low variance hemispheres: WMAP 3 few% Net : < 10-7

Planck vs. WMAP MPV Important to remove Doppler quadrupole As Martin Quantin reminded us …Important to remove Doppler quadrupole Important to remove Doppler quadrupole

Planck vs. WMAP MPV

Quadrupole+Octopole Correlations Cosmology (“Physical Model”) but how to get dipole correlation? how to get C2 < C3 ? Systematics how do you get such effects? esp., how do you get a N-S ecliptic asymmetry? (dipole mis-subtraction?) how do you avoid oscillations in the time-ordered data? how do you get the systematics in both WMAP and Planck The Galaxy: (Systematics/Physical Model) has the wrong multipole structure (shape) is likely to lead to GALACTIC not ECLIPTIC/DIPOLE/EQUINOX correlations Other Foregrounds -- difficult: Changing a patch of the sky typically gives you: Yl0 Sky has 5x more octopole than quadrupole How do you get a physical ring perpendicular to the ecliptic Caution: can add essentially arbitrary dipole, which can entirely distort the ring! (Silk & Inoue) How do you hide the foreground from detection? T≈TCMB

Conclusions? How to make progress? Alignments are: Persistent Individually interesting, collectively significant but hard to explain, or establish “priority” How to make progress?

The uncorrelation …

“The Low-l Anomaly” The low quadrupole

“The Large-Angle Anomaly”

Angular Correlation Function C() C() = < T(T)>cos But C() = l Cl Pl(cos ())  Same information as Cl, just differently organized Why should C() be interesting?

Two point angular correlation function -- WMAP3

The Large-Angle Anomaly: Is it Significant? One measure (WMAP1): S1/2 = -11/2 [C()]2 d cos 

Statistics of C(θ)

Origin of C(θ)

Only 5% of LCDM realizations have low a full-sky S1/2 Is it an accident? Only 5% of LCDM realizations have low a full-sky S1/2 Only 2% of rotated and cut full skies with such low full-sky S1/2, have this low a cut-sky S1/2

Statistics of C(θ) 0.03-0.1% of realizations of the concordance model of inflationary ΛCDM have so little cut sky large-angle correlation ! Either: this reflects a <0.1% probable full sky C(θ), or a 5% probable C(θ) and a 2% probably alignment with the galaxy

Did this change in Planck?

CR minimal mask Kq75y9 mask

Planck R1 Copi, Huterer, Schwarz, GDS arxiv 1310.3831 MNRAS (in press) Full sky expected 50,000 Copi, Huterer, Schwarz, GDS arxiv 1310.3831 MNRAS (in press)

S1/2 vs. Cl S1/2 is NOT small (just) because C2 is small, nor because Cl are small but because C2, C3, C4, C5 cancel C6,… “The steep, nearly linear rise in the spectrum from l = 2 to 5 translates to a near absence of power in the angular correlation function at separations larger than ~6[0]° (Spergel et al. 2003; Bennett et al. 2003b). This was also seen in the COBE DMR data, but it is now clear that this is not due to Galaxy modeling errors.” WMAP team – Yr 1 Figure 1. Two-point angular correlation function from the inpainted Planck SMICA map. The black, dotted line shows the best-fitting ΛCDM model from Planck. The shaded, cyan region is the 68 per cent cosmic variance confidence interval. Included from the SMICA map are the C(θ) calculated on the full-sky (black, solid line) and from two cut skies using the U74 mask (green, dash-dotted line) and the KQ75y9 mask (red, dashed line). See the text for details. http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/powspec/wmap_gh2_images.cfm

Violation of GRSI Even if we replaced all the theoretical Cl by their measured values up to l=20, cosmic variance would give only a 3% chance of recovering this low an S1/2 in a particular realization and most of those are much poorer fits to the theory than is the current data

Explanations This is a statistical fluke in standard LCDM It’s physics! Possible physics implications: R(r)Ylm(Ω) are wrong basis to preserve Gaussianity Examples: a) cosmic topology (=> eigenmode basis) b) ξ(|x1-x2|>R)=0 (=> compact support basis)

Low Northern Variance Power asymmetry Dipole modulation Compare S vs N. North looks much “quieter” Low Northern Variance

Expanded/confirmed/… by many: “Eriksen et al. (2004) and Hansen et al. (2004) … discovered that the angular power spectrum of …WMAP[1] data, when estimated locally at different positions on the sphere, appears not to be isotropic.” Planck 2013 XXIII. Expanded/confirmed/… by many:

Compare S vs N. North looks much “quieter”

SMICA N vs S variance Temperature variance distributions for the unconditioned-CDM realizations considering two dffierent sky coverage scenarios: pixels in the northern Ecliptic hemisphere (Ecliptic-North, left), southern Ecliptic hemisphere (Ecliptic-South, middle) and the portion of the northern Ecliptic hemisphere that can be seen from the Chilean Atacama site (Atacama-North, right). The vertical lines represent the corresponding values calculated from the Planck SMICA temperature map with p-values displayed in the plot legends. The Ecliptic-North temperature data has an anomalously low variance (p = 0:1 per cent) when compared with unconditioned-CDM while the Ecliptic- South appears unremarkable (p = 42:3 per cent). The north variance p-value increases to 1:0 per cent when only the Atacama-North pixels are considered. See section 2.2 for parameters. p ~ 0.001

And … A couple of more that I find intriguing

Advances in Astronomy, vol. 2012, id. 960509

Angular Power Spectrum At least 3 other major deviations in the Cl in 1st year data

Power spectrum: ecliptic plane vs. poles “First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: The Angular Power Spectrum” G. Hinshaw, et.al., 2003, ApJS, 148, 135 -- only v.1 on archive NOTE: S/N of these (especially at peak) are not high. All 3 other major deviations are in the ecliptic polar Cl only!!

With so many anomalies, what do we do? Compare S vs N. North looks much “quieter”

Making Progress Find a fundamental physics model, make testable predictions & test them. Make predictions from reasonable phenomenological extrapolations & test them. Adopt the “fluke hypothesis,” use it to make predictions & test them.

New Models List of of new fundamental physics models that explain (multiple) anomalies:

Phenomenological extrapolations Philosophy: assume each anomaly is “real” and guess what that implies for other observables

Testing the fluke hypothesis Philosophy: assume LCDM is correct, and see how the measured anomalies affect predictions for other observables. Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.

Constrained realizations (testing the fluke hypothesis) Create realizations of (best-fit) ΛCDM Constrained to agree with observed T anomalies Better: constrained to agree with observed maps. Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations. Augment with realizations of other physical quantities with correct covariance (eg. polarization, lensing potential)

Testing the fluke hypothesis + Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations. Phenomenological extrapolations

Low northern variance

Phenomenological guess Low variance in T over a large region of the sky should imply low variance in polarization (at least E-mode) in that same region

After all, T-E are correlated! What does LCDM say? After all, T-E are correlated! Solid: LCDM LCDM conditioned on SMICA map.

a small reduction in the polarization variance Solid: LCDM LCDM conditioned on SMICA map. Observe: a small reduction in the polarization variance approximately equal in N and S

Test of the phenomenological guess Recall: T variance was 10% supressed! Look for reduced variance in North Ecliptic E 10% variance suppression => extremely low p-value

Example 2: Absence of two-point angular correlation Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.

Phenomenological guess Absence of angular correlation in T implies absence of angular correlation in polarization (at least E, and so Q and U Stokes parameters)

What does LCDM say? If CTT(θ>60)~0 is a fluke, other correlation functions are affected (Dvorkin, Peiris & Hu 2008) Solid: LCDM LCDM conditioned on SMICA map.

Predicted TQ correlations CTQ(θ>60)~0 is affected Figure1.Histogram of ST(23-174) values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations. but signficant correlation is still “expected”

Constrained-LCDM QQ and UU correlations A. Yoho, A. Aiola, C. Copi, A. Kosowsky, GDS (PRD91 (2015) 12, 123504) Implication – if the absence of TT correlations at large angles is due to an absence of \Phi\Phi correlations at large distances, then this should result in an absence of QQ/UU correlations

Predicted (local)E/B-mode correlations Implication – if the absence of TT correlations at large angles is due to an absence of \Phi\Phi correlations at large distances, then this should result in an absence of QQ/UU correlations Phenomenological guess of suppressed S1/2QQ or S1/2UU would be unlikely in LCDM if low enough. (Suppression of <1/20 in TT.)

Phenomenological guess Absence of angular correlation is due to absence of spatial correlation in 3d Consequence: expect low/no correlation in: (T, E, B?, φ, δ(z), …) x (T, E, B?, φ, δ(z’), …)

Eg. T-lensing correlations Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations. LCDM predicts mild suppression of Tφ

Another phenomenological prediction -- the cosmological dipole C(θ) has had the monopole and dipole subtracted. If C(θ>60)~0 is physical, then the cosmological dipole must be small C1 < ~ 200 (μK)2 (C1th ~ 3300(μK)2 ) Q: can you detect the/this dipole?

SUMMARY The (low-l) sky appears NOT to be a realization of a Gaussian random statistically isotropic field.

SUMMARY The T sky lacks large-angle correlations Temperature multipoles are aligned with one another and/or with the ecliptic/dipole The T sky lacks large-angle correlations There are noticeable hemispherical asymmetries/differences etcetera

No good “model” so far: Systematics Foregrounds Cosmology

They’re trying very hard to hush it up. While the cosmic orchestra may be playing the LCDM symphony, somebody gave the bass and tuba the wrong score. They’re trying very hard to hush it up. There is no good theory for any of this, yet! But we may be able to test explanations anyway.