coles deus
DESCRIPTION
Talk on "Cosmic Anomalies" by Peter Coles given at the Conference "Current and Future Challenges of the Dark and Early Universes", Niels Bohr Institute, Copenhagen, 8-12 August 2011.TRANSCRIPT
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Cosmic AnomaliesPeter Coles
(Cardiff)DEUS, Copenhagen,
Tuesday 9th August 2011
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Part I:Rambling Introduction
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“CONCORDANCE”
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Theory (, n, H0…)
Observations
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There are many ways of being weird
• Initial Perturbations:
• Non-stationary fluctuations, e.g. statistical anisotropy from a vector field?
• Global inhomogeneity or anisotropy• Non-trivial topology, etc…
22LLNLL f
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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.”
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Part II:CMB Anomalies
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Weirdness in Phases
0
),(),(,l
lm
lm lmYaTT
ml
mlmlml iaa ,,, exp
For a homogeneous and isotropic Gaussian random field (on the sphere) then the phases are independent and uniformly distributed.
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Types of CMB Anomalies• Type I – obvious problems with data
(e.g. foregrounds)• Type II – anisotropies (North-South, Axis
of Evil..)• Type III – localized features, e.g. “The
Cold Spot”• Type IV – Something else (even/odd
multipoles, magnetic fields, ?)
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(from Hansen et al. 2004)
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(from Copi et al. 2005)
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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.
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)!|()|( AMPMAP
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“If tortured sufficiently, data will confess to almost
anything”
Fred Menger
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Is there an Elephant in the Room?
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A. There’s no problem at all with CDM…
B. There are interesting indications…
C. There’s definitely evidence of new physics
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Part III:Extreme Objects
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Extreme Value Statistics (exact)
)....sup( 1max ni XXXX
Given the distribution of X, what is the distribution of Xmax?
1
21max
)()()(
)(
)(...)()(),...,Pr()Pr(
n
n
n
zFznfzp
zF
zFzFzFzXzXzXzX
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Extreme Value Statistics(asymptotic)
n
n
abzzG
naszGzX
expexp)(
)(Pr max
For any distribution of exponential type, in the sense that
0)(
)(1lim
xfxF
dxd
x
Then there is a stable asymptotic distribution
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Comments• There are two other stabe asymptotes• Some distributions converge very slowly
(e.g. Gaussian)• The X may be correlated. • Only weak discriminatory power for non-
Gaussianity in asymptotic form; better to use “exact” behaviour, see Harrison & Coles (2011)
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Mass Function
),,(1
log)(
2exp12)(
1
2
2
2
2
cNL
c
c
p
c
c
fR
dMd
mf
dMdn
aa
Aaf
e.g. Sheth & Thormen:
Correction for primordial non-
Gaussianity
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Waizman, Ettori & Moscardini, 2001 arXiv:1105.4099
See also: Colombi et al. 2011; Davis et al. 2011
1
1exp)( yyF
These use alternative parametrisation
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