PoS(Cosmology2009)011 . o http://pos.sissa.it/ Cold – and is the single most Λ ∗ [email protected] [email protected] [email protected] [email protected] Speaker. This lack of correlation is unlikelyrandom to statistically be isotropic present modes in proportional astandard to model. which spherical is harmonics, a as realization is of predicted Gaussian by the The measured fluctuations intools cosmic for microwave studying background . radiation Itthe is is standard widely one portrayed model of as of the providing cosmology extraordinary principal – confirmation of inflationary important data set for determining theportion parameters of of the that model. CMB fluctuations, However,Microwave the as Anisotropy large-angle/low-l measured Probe, most display recently featuresfully-reconstructed and that sky completely are demonstrates by at a the odds peculiarcomponents Wilkinson of with alignment the the fluctuations of with standard each the other. model. quadrupoleperpendicular Moreover, those to and aligned the The multipoles the ecliptic define a plane, octopole plane andrather apparently precisely pointing separates toward the the strong CMB extrema dipole. ofof the The southern the ecliptic ecliptic northern sky from ecliptic the weaker sky.demonstrates extrema an If unusual the lack reconstructed of sky correlation behind for the pairs galaxy of directions is separated excluded, by the more CMB than 60 ∗ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

International Workshop on Cosmic Structure andSeptember Evolution 23-25, - 2009 Cosmology2009, Bielefeld, Germany Dominik Schwarz Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany E-mail: Craig J. Copi Dept of Physics/CERCA/ISO, Case Western Reserve10900 University Euclid Ave, Cleveland, OH 44106-7079E-mail: USA Dragan Huterer Department of Physics, University of Michigan, 450 Church St, Ann Arbor, MIE-mail: 48109 USA Glenn Starkman Dept of Physics/CERCA/ISO, Case Western ReserveCleveland, University OH 44106-7079 USA E-mail: Is the large angle CMB Inconsistentconcordance cosmology? with PoS(Cosmology2009)011 K, (1) (2) o ’s. l C K. This glow o Glenn Starkman , ) φ ], although other maps (LILC, TOH, , . 1 2 θ | ( m , m , l l a T Y | m ∆ , m l ∑ a CDM – of statistically independent 2 1 m Λ , l ∑ + 1 l 2 ) = 2, since the dipole is dominated by the Doppler contribu- φ = , l ≥ θ l C ( T ∆ ]) are available. These results are only slightly dependent on the choice of maps. 2 We thus write for the temperature fluctuations, One of the first lessons in cosmology kindergarten is that when presented with a continuous When we look at the sky in the microwave band, we have, since Penzias and Wilson in the We’ve also known, pretty much since then, that that cosmic microwave radiation ought not to The road to discovery of the CMB anisotropies was longer and harder than was first antic- The modern standard in CMB anisotropies is the Wilkinson Microwave Anisotropy Probe tion due to the motion ofpower the spectrum Sun is and the satellite through the microwave background. The angular NILC [ where the sum is generally taken over function on the sphere offunction the in sky spherical (as harmonics. opposedby to This various a groups applies catalogue from to of the thefaithfully objects) individual reconstruct WMAP one the band full CMB should maps sky temperature expand releasedWMAP maps over that by that the team’s the full are own WMAP sky. synthesized Internal team We Linear shall in focus Combinations an our map attempt attention to [ on the 1960s, seen an isotropic glow characterized by an antenna temperature of about 3 be perfectly homogeneous, After all, the universe todayaround is the awfully lumpy room – as – we canuniverse. and see by Indeed, that looking the lumpiness most shouldis reasonable be that explanation evident it for developed even the through in currentseeds the of inhomogeneity this action structure of fossil of should the be gravity record universe evident from of in earlier the the primordial CMB. early inhomogeneities. These ipated. A dipolarthrough anisotropy the caused, universe, presumably, was discovered byplorer in (COBE) the in the Doppler the 1970s; early effect but 1990ssignificant due for it enough compelling took to to evidence until of earn Earth’s primordial the the motion anisotropies project Cosmic – leaders Background a the discovery Ex- 2006 Nobel Prize(WMAP). in Physics. This satellite, launched inlikely to 2001, be provides, displaced at by the leastdiscuss for what satellite, we the the can next best learn few fullwill about sky months identify the maps the when original of largest low-l it the problem angle is CMB. –power properties the In spectrum. smallness of this Motivated of the talk by the I CMB quadrupole that, component will we fromand of will WMAP the octopole, examine angular data. the discovering more that We detailed they structuredirections seem of unexpectedly or the aligned quadrupole structures with on eachwill the other return sky and to with that the physical are low-l probleminstead associated and of with realize l-space, the that and that it WMAP it isthe experiment. presents far standard a more cosmological Finally, serious serious model challenge we – when to inflationary viewed the in absolutely angle-space canonical prediction of How the CMB challenges cosmology is the relic radiation ofcomparable a to time when the the surface universe temperatureof was of the younger, a denser Big star. and Bang theory hotter Its ofcooling – discovery from cosmology about was an – 3000 therefore initially the confirming hot theory dense evidence that state. we live in a universe that is expanding and PoS(Cosmology2009)011 1) (3) , 992 0 . , 0 1 < − Ω obeys: = − and a small- m lm 1 l ( a Glenn Starkman C > m ) is anomalously 1 2 a C 0179 . unit vectors and a single l 72, and 1 . 1 in terms of 0 = ' ] an old idea dating back at least to l 1 . 5 l − h C 0 mm CDM is remarkable. One of the first things δ 0 Λ , can be replaced by ll l δ , where by 3 l Ω = C i ], just shy of the diameter of the horizon. Of course, − 0 4 m 1 , 0 ∗ l √ a / CDM to be (very nearly) independent Gaussian random m , l Λ of any given a . While there have been some claims of discovery of cosmic l h even though the scale of topology is larger than the horizon MpC C lm 1 l a − C ]. 1 h 6 + l are predicted by the theory. l C ]. 3 are predicted by inflationary lm a One can show that the 2 As an explanation for the smallness of the quadrupole, the argument for the utility of a compact Nevertheless, the possibility of cosmic topology is a legitimate one. And it certainly could Is there anything else to learnThe about first the universe thing on that large scales? suggested that there may be was the observation already by the Cosmic Whatever the explanation for the low quadrupole, we are motivated to look beyond just the It is by now well known that the agreement between the observed WMAP Maxwell of multipole vectors [ scalar. These unit vectors (whose sign can be absorbed into the scalar) are termed multipole vectors. topology, they are notclosed widely null accepted. geodesic be longer The than best 24 GpC reported [ limits on it require that the shortest universe is that if the universecation is scale compact, cannot then modes be with supported wavelengthwill by larger result the than in space. the a compactifi- This reduction reduction ofreason, in the not the large the number scale least power. of of Unfortunately largeequal which this scale amplitudes by argument is modes inflation. is that However, flawed if it for we reliesmakes are many seeing no on the reliable an full predictions extent assumption for of that the the universe all amplitude then of modes inflation modes are of populated that with lead wavelength. to unexpected values for low-l low. This observation was confirmedrenewed interest by in WMAP. cosmic One topology thing –curves that the that this possibility cannot observation that be smoothly the spawned collapsed universe was towe in a a live which point. in we a Or, live as small has some or closed prefer compact to universe. put it, the possibility that topology could affect the low-l Background Explorer (COBE) team in the early 1990s that the quadrupole ( angular power spectrum to seeanomalies if have the been low-l noted multipoles with arenot regard list otherwise to them well the here, behaved. not low-l/large-angle because In propertiesspace. they fact, Suffice of are it many the to not CMB. say interesting, that We butof each shall because anomalies in they its that are own I too way would retells numerousIn some like for of analogy to this the discuss with ensuing grew story. the out The interchangeability particular of of set the the search description for topology of beyond the horizon. diameter. This would make this explanation that much more difficult to test. How the CMB challenges cosmology The with a description in termsdirections, of a with dipole the vector, idea wemultipoles. sought that to somehow With describe the this the in topology l-th multipole mind would by we correlate special unwittingly the reinvented directions [ of different variables, and to be statistically isotropic. This means that the ensemble average of The expected values of at the 95% CL [ dimensional parameterization of the predicted we learn is that thegeometry universe is is approximately very 3000 close to a flat geometry. Indeed the radius of curvature of the PoS(Cosmology2009)011 ]. 11 describing CDM [ m Λ 3 a Glenn Starkman ]. Indeed, the ob-

9 ] under the assumption that 8 , 7 [ et al. and by a pair of multipole vectors. (Or, the unlikely alignment of the quadrupole 2 C , and a pair of multipole vectors which are in- 2 given C 4 ], we showed that these planes are surprisingly perpendic- 11 and by three multipole vectors. The octopole can therefore be 3 C 2 and 3 multipoles. The solid curve is the ecliptic plane. which depends on = 2 l A The .) The quadrupole can thus be thought of as a plane. Similarly, the 7 ]. The normal to these planes was later termed the "Axis of Evil", a mild misnomer of the quadrupole are thus replaced by 2 Figure 1: ] and the more detailed [ m 9 C should be uncorrelated. 10 2 l a are Gaussian random and statistically isotropic. Certainly, however, the multipole vectors lm It is difficult to understand how cosmological physics could have produced these alignments If these alignments among the planes of the octopole and the quadrupole were the end of The 5 a and octopole planes, was at mostmal 2%. points Furthermore, surprisingly the close plane to is the oriented(relative dipole to in – the such the CMB) a direction – way of that which themation, its just Sun’s the nor- happens motion quadrupole to through plus lie the octopole near universe can thesix be ecliptic. extrema described that Finally, as to are a a evenly ring spaced very (defined aroundvery good by the approxi- carefully this ring. threads common This its plane) ring of way ofthree between six weakest. is them, so The thus positioned picture separating that of the the this three ecliptic (Figure strongest 1) extrema is from rather the remarkable. served degree of alignment is seenThis in phenomenon only was about first 0.1% of describedintuitive) in realizations (albeit [ of using inflationary other statistics, which we of course find less ular to the ecliptic – thethat plane this of alignment the would Earth’s happen (and by WMAP’s) orbit chance, around even the Sun. The probability since there is no axial symmetryinstead of the the Plane multipoles of around Pain. their normal. Perhaps it should be called the story then it might suggestHowever, in that [ the explanation is some rather odd cosmological phenomenon. Their statistical properties have been calculated by Dennis more accurately by a scalar thought of as three planes.calculated The for three planes the of ILC the map octopole turn and out the plane to of be the surprisingly quadrupole parallel when to each other [ the of different dependent of the octopole can be replaced by How the CMB challenges cosmology PoS(Cosmology2009)011 . 0 l 2 Y (5) (4) C ) = ]. θ ( 13 C .) CDM [ Glenn Starkman in the five year θ Λ ) θ ( comes from pairs of C o ], which also show how 15 measured outside that mask is 2 ] and [ / . equivalent to the smallness of 1 θ CDM with the standard parameter 14 S , Λ θ cos not = 2 is cos Ω · 2 1 d / 1 Ω 2 | S ) )) 2 θ Ω ( ( 5 C ( T ) 2 1 / 1 1 Ω − ( Z T = ≡ 2 / ) 1 θ S ( . On a full sky they contain the same information, and l C C . However, this anomaly was not terribly statistically significant. Had o ] that this reflects largely a change in what is reported. If, as in the first ] noted that the two point correlation function seemed to be unexpectedly 15 12 . However, one should be cautious in jumping to the conclusion that therefore with the appropriate choice of z-axis. Explanations which yield aligned ) ll θ Y cos ( l P l is closely related to ]. Back in those times, it was not yet unusual to plot, not just the angular power spectrum, C ) ) 12 1 θ ( over the whole sky, one finds that almost all the contribution above 60 + Having identified the aforementioned mysterious alignments, let us return to the original ob- Since then, the anomaly has appeared to largely go away in the reported WMAP results. How- The authors of [ C ) l 2 θ , which offers a more direct window into inflationary theory, is always the correct set of variables. ( ( l this is unlikely to beand an octopole. accident It of is also the showed galaxy that happening the to smallness overly of the power in the quadrupole was observed to be smaller than in approximately 0.1% of random realizations of WMAP data is largely unchanged from the first yearpoints data. at least Indeed, one in ofso which the small is ILC, that inside if only the one in KQ75values calculates about galaxy does it 0.03% mask. come of out random smaller. realizations This of is discussed at length in [ year WMAP analysis, one extracts the angularoutside correlation the function galaxy directly (for from example the part outside of the the KQ75 sky mask), then one finds that they done a statistical analysis (whichthe they correlation do function not at seem large to anglesnow-concordance remains have done), cosmology. this close they The to would WMAP zero have team found intheir about that confirmed first 5% this year of anomaly of realizations in observations. of the The our anomaly, papers as describing quantified by the statistic they proposed, servation of a small quadrupole and askpower whether spectrum. that A is hint really to the the salient answer featurepapers to in [ that the question low-l was angular provided by one of the later COBE-DMR close to zero above about 60 ever, we have shown [ are not adequate. Finally,quadrupole. the observed Therefore power explanations in which theunlikely involve octopole expansions to in is succeed vectors comparable if of toquadrupole. small the the magnitude power octopole are in results the from a higher order in the expansion than does the but the two point correlation function How the CMB challenges cosmology with the solar system, except byhow some foregrounds unkind could coincidence. have But done itthen it. is the no CMB In less signal particular difficult to must ifprise. understand be the Moreover, the smaller aligned multipole than signal structure the of ismultipoles the foreground. due – observed to quadrupole ie. This and the in octopole foreground, is and aligned of planar itself would be a sur- (The overbar indicates a sky average over all pairs of points separated by an angle This would be analogous to sayingdomain, never that in one the should time always domain. look at some time series in the Fourier ∑ C C PoS(Cosmology2009)011 , 79 , 295 367 399 are Gaussian . Thus a small Glenn Starkman ) , 063516 (2004) lm θ a 69 ( , 084034 (2007) C 75 , 221301 (2004) 93 , 330 (2009) [arXiv:0803.0547 , 023507 (2007) – in which the contributions from 75 A&A 493, 835-857 (2009) . 180 5 C , 043515 (2004) [arXiv:astro-ph/0310511]. et al. 70 , and 4 . The reason is that even if we change the l C C , 3 very close to zero, the process of drawing gaus- C , ) sufficiently different from the theoretical expecta- 6 2 l θ ( C C C , 1653 (2005) [arXiv:math-ph/0410004]. 38 will yield measured l Astrophys.J. 612 (2004) 633-646; TOH: M. Tegmark, A. de Oliveira-Costa and A. C [WMAP Collaboration], Astrophys. J. Suppl. et al. et al. by hand to make the expected l C with variance lm [arXiv:astro-ph/0403353]. [arXiv:astro-ph/0307282]. (2006) [arXiv:astro-ph/0508047]. [arXiv:astro-ph/0605135]. (2009) [arXiv:0808.3767 [astro-ph]]. astro-ph/0302209. by Dover Publications, 1954. [arXiv:astro-ph/0604616]. Microwave Background Data Analysis at http://lambda.gsfc.nasa.gov/product/map/dr3/ilc_map_get.cfm [astro-ph]]. Hamilton, PRD 68, 123523 (2003); NILC: J. Delabrouille challenges a most fundamental prediction of standard cosmology – that the Perhaps the most intriguing aspect of this is that the small two-point correlation function can- a 2 / 1 [7] M. R. Dennis and K. Land,[8] arXiv:0704.3657 [astro-ph]. M. R. Dennis, J. Phys. A [5] C. J. Copi, D. Huterer and[6] G. D. James Starkman, Phys. Clerk Rev. Maxwell, D A Treatise on Electricity and Magnetism, 1st ed. 1873, 3rd ed. 1891, reprinted [9] D. J. Schwarz, G. D. Starkman, D. Huterer and C. J. Copi, Phys. Rev. Lett. [3] E. Komatsu [2] ILC: Eriksen [4] J. Shapiro Key, N. J. Cornish, D. N. Spergel and G. D. Starkman, Phys. Rev. D [1] The WMAP team’s Internal Linear Combinations map is available from NASA’s Legacy Archive for [10] A. de Oliveira-Costa, M. Tegmark, M. Zaldarriaga and A. Hamilton, Phys.[11] Rev. D C. J. Copi, D. Huterer, D. J. Schwarz and G. D.[12] Starkman, Mon. G. Not. Hinshaw Roy. Astron. et Soc. al., Astrophys. J.[13] 464, L25 D. (1996), N. astroph/ Spergel 9601061. et al., Astrophys.[14] J. 148, C. S175 Copi, (2003), D. Huterer, D. Schwarz and G. Starkman, Phys. Rev. D [15] C. J. Copi, D. Huterer, D. J. Schwarz and G. D. Starkman, Mon. Not. Roy. Astron. Soc. sian theoretical not be obtained merely by changing the theoretical those multipoles cancel those fromcorrelation higher function multipoles there – actually to is. explain how little large angle two point tions so as to reduce theS precise cancellations that go into getting a very small How the CMB challenges cosmology Indeed, it appears to require the conspiracy of random and statistically isotropic (GRSI).suggests So that far GRSI this is may acosmology be will 98% ruled demand C.L. even out statement, more at but strongly some much ongoing modification work greater on confidence. large scales. References If so, our standard model of