coles deus

Cosmic AnomaliesPeter Coles

(Cardiff)DEUS, Copenhagen,

Tuesday 9th August 2011

Part I:Rambling Introduction

“CONCORDANCE”

Theory (, n, H0…)

Observations

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

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.”

Part II:CMB Anomalies

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.

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, ?)

(from Hansen et al. 2004)

(from Copi et al. 2005)

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.

)!|()|( AMPMAP

“If tortured sufficiently, data will confess to almost

anything”

Fred Menger

Is there an Elephant in the Room?

A. There’s no problem at all with CDM…

B. There are interesting indications…

C. There’s definitely evidence of new physics

Part III:Extreme Objects

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

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

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)

xexpexp

PDF

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

Waizman, Ettori & Moscardini, 2001 arXiv:1105.4099

See also: Colombi et al. 2011; Davis et al. 2011

1

1exp)( yyF

These use alternative parametrisation