Cosmic Anomalies Observational measurements of the temperature variation of the Cosmic Microwave Background across the celestial sphere made by the Wilkinson Microwave Anisotropy Probe (WMAP) and, more recently Planck, have played a major part in establishing the standard "concordance" cosmological model. However, extensive statistical analysis of these data have also revealed some tantalising anomalies whose interpretation within the standard framework is by no means clear. In this talk, I'll discuss the significance of the evidence for some aspects of this anomalous behaviour, offer some possible theoretical models, and suggest how future measurements may provide firmer conclusions.

1. Cosmic Anomalies
Peter Coles
(University of Sussex)
Kobayashi-Maskawa Institute, Nagoya
Thursday 16th January 2014

8. The Meaning of Inflation (OED)
1. The action of inflating or distending with air or
gas
2. The condition of being inflated with air or gas,
or being distended or swollen as if with air
3. The condition of being puffed up with vanity,
pride or baseless notions
4. The quality of language or style when it is
swollen with big or pompous words; turgidity,
bombast

9. “CONCORDANCE”

11. Planck Time!

14. Theories
Bayesian
Frequentist
Observations

15. Cosmology is a very
efficient exercise in data
compression...
Cosmology is an exercise in data compression
….but it is always worth
looking at the information
thrown away to check
that nothing has been
missed!

16. Precision Cosmology
“…as we know, there are known knowns;
there are things we know we know. We
also know there are known unknowns;
that is to say we know there are some
things we do not know. But there are
also unknown unknowns -- the ones we
don't know we don't know.”

17. Is there an Elephant in the Room?

18. How Weird is the Universe?
• The (zero-th order) starting point is
FLRW.
• The concordance cosmology is a “firstorder” perturbation to this
• In it (and other “first-order” models), the
initial fluctuations were a statistically
homogeneous and isotropic Gaussian
Random Field (GRF)
• These are the “maximum entropy” initial
conditions having “random phases”
motivated by inflation.
• Anything else would be weird….

19. Precision Cosmology
“…as we know, there are known knowns;
there are things we know we know. We
also know there are known unknowns;
that is to say we know there are some
things we do not know. But there are
also unknown unknowns -- the ones we
don't know we don't know.”

20. There are many ways of
being weird!
• Initial Perturbations:
[
2
2
Φ=Φ L +f NL Φ L −〈Φ L 〉
]
• Non-stationary fluctuations, e.g.
statistical anisotropy from a vector
field?
• Global inhomogeneity or anisotropy
• Non-trivial topology, etc…

21. Weird Topology
• GR is a local theory
• Simplest topology
chosen in standard
models, e.g sphere.
• Small universes
suppress power on
large scales…but
introduce phase
correlations (Dineen,
Rocha & Coles,
MNRAS, 358, 1285)

22. Fourier Phases
δ ( x )=∑ δ( k )exp (ik⋅x )
• The usual thing
k
δ (k )=∣δ (k )∣exp [ iϕk ]
• where
• In a homogeneous and isotropic GRF then
the phases
are ϕ
random...
✳
• ..apart from
δ (k )=δ(−k )
ϕ k −ϕ k
• ..as are differences, e.g.
• The power spectrum
2
1
2
P( k)∝〈∣δ( k)∣ 〉

24. The Bispectrum
• The power spectrum is blind to phase information
• Phase information is encoded in an infinite
hierarchy of polyspectra, e.g. the bispectrum:
✳
〈δ (k 1 )δ (k 2 )δ ( k 1 + k 2 )〉=〈δ( k 1 )δ( k 2 )δ (−k 1 −k 2 )〉
• Averaging is done over triangles in k-space
• This measures a specific form of phase coupling;
quadratic phase coupling, so it is tailor-made for
quadratic non-Gaussianity

25. Quadratic Phase Coupling
k2
k1
−( k 1 + k 2 )
δ 1 =exp(i k 1⋅x +φ 1 )⇒( k 1 ,φ 1 )
δ 2 =exp(i k 2⋅x +φ2 )⇒( k 2 ,φ 2 )
2
(δ 1 +δ 2 ) ⇒(2 k 1 , 2φ1 )+ (2 k 2 , 2φ 2 )+ ( k 1 + k 2, φ 1 +φ2 )
arg ( δ 1 δ 2 δ −( 1+ 2 ) )=φ1 +φ 2 −φ1+ 2

27. Weirdness in Phases
ΔT ( θ,φ )
=∑ ∑ a l,m Y lm ( θ,φ)
T
a l,m =∣al,m∣exp [ iϕl,m ]
For a homogeneous and isotropic Gaussian random field
(on the sphere) the phases are independent and
uniformly distributed. Non-random phases therefore
indicate weirdness..

28. Spherical Harmonic Phases
• The
•
•
•
•
ΔT ( θ,φ )
=∑ ∑ a l,m Y lm ( θ,φ)
T
usual thing
where a l,m =∣al,m∣exp [ iϕl,m ]
If the fluctuations are a homogeneous
and isotropic GRF then the phases
are random... ϕl,m
..apart from a ✳ =al,−m
lm
ϕ l,m −ϕ l,m−1
..as are differences, e.g.

29. Zonal
(m=0)
Sectoral
(m=l)

36. Theories
Bayesian
Frequentist
Observations

37. Suspects
Evidence

38. Beware the Prosecutor’s
Fallacy!
P( A∣M )≠P ( M∣A )!

39. “If tortured sufficiently, data
will confess to almost
anything”
Fred Menger

41. Types of CMB Anomalies
• Type I – obvious problems with data
(e.g. foregrounds)
• Type II – anisotropies and alignments
(North-South, Axis of Evil..)
• Type III – localized features, e.g. “The
Cold Spot”
• Type IV – Something else (even/odd
multipoles, magnetic fields, ?)

45. m
l

48. Low Quadrupole?

50. Parity Violation?

51. (from Hansen et al. 2004)

52. (from Copi et al. 2005)

54. Hanson & Lewis, arXiv:0908.0963

57. Global Asymmetry?
• It has been suggested that the answer may
be departure from FRW cosmology, e.g.
Bianchi (homogenous but anisotropic)
• This can trivially solve the quadrupole
problem (e.g. Bianchi I is a pure quadrupole)
• Such models produce a specific polarization
pattern which is set by the temperature
pattern.
• These (almost) inevitably have a large Bmode…
(Pontzen & Challinor 2007; Pontzen 2009; Sung & Coles
2009; Sung & Coles 2010)

58. Friedman-Robertson-Walker

59. Temperature
Bianchi vectors
Scalar curvature
Bianchi I
a =0, ni =0
R =0

60. Temperature
Bianchi vectors
Scalar curvature
Bianchi V
a ≠ 0, ni = 0
R = −6a 2

61. Bianchi V
Polarization
Amplitude
Stokes parameter:
Q and U

62. Temperature
Bianchi vectors
Scalar curvature
Bianchi VII0
a = 0, n1 = 0, n2 = n3 ≠ 0
R=0

63. Bianchi VII0
Polarization
Amplitude
Stokes parameter:
Q and U

64. Temperature
Bianchi vectors
Scalar curvature
Bianchi VIIh
a ≠ 0, n1 = 0, n2 = n3 ≠ 0
R = −6 a 2

65. Bianchi VIIh
Polarization
Amplitude
Stokes parameter:
Q and U

66. Temperature
Bianchi vectors
Scalar curvature
Bianchi IX
a = 0, n1 = n2 = n3 ≠ 0
1 2
2
2
R = (n1 + n2 + n3 )
2

67. Bianchi IX
Polarization
Amplitude
Stokes parameter:
Q and U

70. Wise Words from WMAP (7)
arXiv:1001.4758
In this paper we examine potential anomalies and
present analyses and assessments of their
significance. In most cases we find that claimed
anomalies depend on posterior selection of
some aspect or subset of the data. Compared with
sky simulations based on the best fit model, one
can select for low probability features of the WMAP
data. Low probability features are expected, but it
is not usually straightforward to determine whether
any particular low probability feature is the result of
the a posteriori selection or of non-standard
cosmology…..We conclude that there is no
compelling evidence for deviations from the
LCDM model, which is generally an acceptable
statistical fit to WMAP and other cosmological
data.

71. Summary
• The concordance cosmology has had many
successes, but that doesn’t make it the
Gospel truth.
• There is intriguing evidence suggesting
that the Universe might be more
interesting than we thought..
• Focussing exclusively on measuring
parameters of the standard model may
result in us missing the Elephant in the
Room.

72. A. There’s no problem at all
with ΛCDM…
B. There are interesting
indications…
C. There’s definitely
evidence of new physics