Evidence for Large Scale Anisotropy in the Universe

Pankaj Jain I.I.T. Kanpur

Introduction

• Universe is known to be isotropic at large distance scales

For example, CMB is highly isotropic

• However there are some indications of anisotropy in several data sets Radio polarizations from radio galaxies Optical polarizations from quasars CMB anisotropies

Offset angle RM)

Anisotropy in Radio PolarizationsAnisotropy in Radio Polarizations

Radio Polarizations from distant AGNs show a dipole anisotropy

RM : Faraday Rotation Measure = IPA (Polarization at source)

Anisotropy in Radio PolarizationsAnisotropy in Radio Polarizations

cut |RM - <RM>| > 6 rad/m2

beta = polarization offset angle = polarization angle – galaxy alignment angle

Birch 1982Jain, Ralston, 1999Jain, Sarala, 2003

preferred axis points towards Virgo

averaged over a small region

Rotation Measure Cut

The data consists of all the radio sources for which the observables , , RM exist in the literature

DATA

Full Data: (332 sources)

P = 3.5 %

Using cut: |RM - <RM>| > 6 (265 sources)

P = 0.06 %

Statistical Significance using Likelihood Analysis

• The signal was first noticed by Birch in 1982• It was dismissed by Bietenholz and Kronberg

(BK) in 1984 using a larger data set• However BK did not test for the signal that

Birch found• The signal is parity odd whereas BK tested

for a signal with mixed parity (Jain and Ralston 1999)

HutsemHutseméékerskers EffectEffectOptical Polarizations of QSOs appear to be locally aligned with one another. (Hutsemékers, 1998)

A very strong alignment is seen in the direction of Virgo cluster

1<z<2.3

Preferred AxisPreferred AxisTwo point correlation

Define the correlation tensor

Define

where

is the matrix of sky locations

S is a unit matrix for an isotropic uncorrelated sample

Optical PolarizationsOptical Polarizations

Preferred axis points towards to Virgo

Degree of Polarization < 2%Ralston and Jain, 2004

Cosmic Microwave Background Cosmic Microwave Background Radiation (CMBR)Radiation (CMBR)

It shows a dipole anisotropy with

This arises due to motion of our galaxy

The higher order multipoles arise due to primordial fluctuations

CMBR is highly isotropic

),()cos('),( 0 TTTT

3

0

10'

T

T

5

0

10 T

T

),(),(2

l

l

lmlmlmYaT

TTemperature Fluctuations about the mean

Statistical isotropy implies

Two Point Correlation Function

estimate of Cl :

2||12

1

l

lmlml a

lC

''*

'' mmlllmllm Caa

lC

In harmonic space, statistical isotropy implies

Very high resolution multi-frequency CMB data is available from WMAP

The data is contaminated:

foregrounds (emissions from our galaxy)

detector noise (dominant at high multipoles l )

extragalactic point sources (dominant at high l)

K band 23 GHz

Ka band 33 GHz

Q band 41 GHz

V band 61 GHzW band 94 GHz

WMAP multi-frequency mapsWMAP multi-frequency maps

WMAP Internal Linear Combination (ILC)WMAP Internal Linear Combination (ILC)

The power at l=2 is low in comparison to the best fit CDM model.

This may be explained in terms of a negative bias in the extracted power at low l

(Saha et al 2008)

12

l

nCCC fcl

cl

cleanl

CMB anisotropies also give an indication of large scale anisotropy

Quadrupole and octopole show a preferred axis pointing towards Virgo

Oliveira-Costa et al 2003

Quadrupole

Octopole

Hence we find several diverse data sets, all indicating a preferred axis pointing towards Virgo

Ralston and Jain, 2004

CMB dipole also points towards Virgo

Oliveira-Costa et al 2003Ralston and Jain, 2004Schwarz et al 2004

dipole quad octo radio optical

dipole 0.020 0.061 0.042 0.024

quad 0.015 0.023 0.004

octo 0.059 0.026

radio 0.008

Prob. for pairwise Prob. for pairwise coincidencescoincidences

Ralston and Jain, 2004

The Virgo Alignment

quadrupoleand octopole

dipoleradio

optical

The axis is some times called the Axis of Evil

I think this name is inappropriate

It does not provide any description of the phenomenon

The term ‘evil’ suggests that the phenomenon is undesired

Such sentiments may be relevant in religion but not in science

Axis of Evil

Alternate Title

The Virgo Axis

The Virgo Alignment

Hemispherical Power AsymmetryHemispherical Power Asymmetry

Eriksen et al, 2004, 2007

Try to determine if the extracted power is anisotropic

Model CMB temperature fluctuations as,

T(,) = s(,) [1+ f(,)] + n(,)

Statistically isotropic field

dipole modulation field

detector noise

Eriksen et al claim dipole modulation amplitude = 0.114

P<1% for this amplitude to arise in an isotropic universe

A Cold Spot in CMB data

Cruz et al (2004) claim existence of a cold spot of size about 10o at

(l, b) = (209o, 57o)

This is detected using Spherical Mexican Hat Wavelet Analysis

with chance Probability 0.2%

The Axis of Anisotropy

Cold spot

Dipole modulation axis

Zhang and Huterer (2009) do not find significant signal for the presence of the cold spot

The difference arises due to their use of circular top hat weights and Gaussian weights instead of Spherical Mexican Hat Wavelets

outcome depends on the choice of the basis wavelet functions

Large Scale Coherent Flow

Peculiar velocity distribution of clusters indicates a large scale bulk flow at distance scales of order 800 Mpc

For z 0.25, axis (l,b) = (296 29, 39 15)o

Kashlinsky et al 2008, 2009

A Dipole Anisotropy in Galaxy Distributions

Itoh et al (2009) claim evidence for dipole anisotropy in the galaxy distribution using SDSS data

The amplitude is an order of magnitude larger than expected due to solar motion

The Axis of Anisotropy

Galaxy distribution

Peculiar velocity

High z Supernova Data

• One may also search for anisotropy using Supernova data

• Violation of isotropy is found, but can be attributed to selection effects

• At low significance we find anisotropy with an axis lying in the galactic plane (Jain, Modgil, Ralston 2005)

• This might indicate a bias in the extinction corrections

• Bias in supernova data was found (Jain, Ralston 2004)

High z Supernova Data

• Cooke and Lynden-Bell (2009) find a signal with very low significance with axis roughly towards CMB dipole

General Procedures to test for General Procedures to test for violation of statistical isotropy in violation of statistical isotropy in

CMBCMB

Bipolar Power Spectrum (BiPS)Bipolar Power Spectrum (BiPS)

LMll

MLll

LMll nYnYAnnC )ˆ()ˆ()ˆ,ˆ( 21

,,,21 21

21

21

Hajian and Souradeep, 2003, 2005

Bipolar spherical harmonicscoefficients

LMll nYnY )ˆ()ˆ( 21 21

= )ˆ()ˆ( 21 22212211nYnYC mlml

LMmlml

Clebsch-Gordon coeffs Spherical Harmonics

Bipolar Power Spectrum (BiPS)Bipolar Power Spectrum (BiPS)

00'2/1

' )12()1( MLllllLM

ll lCA Statistical Isotropy

In order to test for Statistical Isotropy, define

02

,','

Mll

LMllL A

Statistical Isotropy L = 0 L > 0

Hajian and Souradeep do not find any violation of isotropy

They search over several different multipole ranges by employing a window function

Copi et al, 2004, 2006, 2007 proposed a test of statistical isotropy by constructing l unit vectors for each multipole l.

This is closely related to a method we introduced.

We associate a covariant frame (3 orthogonal unit vectors) with each multipole l. This characterizes the preferred direction for each multipole.

Ralston and Jain, 2004 Samal, Saha, Jain and Ralston 2008

Covariant FramesCovariant Frames)(|, lamlalm

)(||,)1(

1)( laJml

lll kk

m

ml,

define a linear map or wave function:

= angular momentum operatorskJ

Using Dirac notation :

are eigenvectors of angular momentum operator 2 JandJ z

are the singular values

The set of three orthogonal e defines a preferred frame for the multipole l

*3

1

)(

mk

km uel

Singular value decomposition

Power Entropy :

We associate an entropy with this matrix

)3log(0 S

We define a density matrix

j m

jm

jm

m

km

km

kk*

'*

~

Von Neumann (1932) 22 ~

log~

,)~log(~

trS

1~ tr

isotropy S = log(3)

Power entropy is useful to test for anisotropy in a particular multipole l

Once we have the preferred frames for each l, we can test for alignment of frames among different l

Alignment across different Alignment across different ll-multipoles-multipoles

we construct a matrix X defined by :

lj

l

l

liij eelX ~~)(

max

2max

is the “principal axis”, which means the eigenvector with largest eigenvalue for each l

le~

Isotropy for a range of multipole moments can be tested with the alignment entropy:

))~log(~( XXX trS

is the normalized X matrix.X~

The eigenvector of X corresponding to maximum eigenvalue gives the preferred direction in the chosen multipole range

Using this technique we may test for anisotropy at any multipole value or in a range of multipole values

However we need to account for the search over the multipole range in assigning statistical significance

Due to the large number of possibilities one should interpret the signal seen in any particular range with caution

Results (ILC map, 2 l 50)

• We find significant signal of anisotropy (at 2 sigma) using power entropy

• We find signal for alignment with quadrupole at 2 sigma

Higher l multipoles 2 Higher l multipoles 2 ll 300 300

Here we test for anisotropy using the individual foreground cleaned DAsQ1, Q2, V1, V2, W1, W2, W3, W4

We use maps with Kp2 mask

Results (2 l 300, 150 l 300)

We find signal of strong anisotropy in the Q1 and Q2 DAs. The axis of alignment lies at galactic latitude

b=25o

Hence it most likely arises due to unknown residual foregrounds

We do not find signal of alignment with quadrupole in this range in any DA

The DAs V1, W1, W2, W3 instead show an improbable degree of isotropy with

P 0.75%, 0.02 %, 0.01%, 0.01%

(150 l 300, using alignment entropy)

We do not understand the cause of this. It may be due to incorrect modeling of detector noise. The problem disappears if we reduce detector noise by about 25%

We have also applied our analysis to the foreground cleaned polarization maps (2 l 300)

We find a very strong signal in almost all the DAs

The axis points in the same direction as the axis found for Q-band temperature maps.

We found that the signal disappears if we enhance the mask applied to the data.

However the axis continues to point in the same direction

The Axis of Anisotropy

Physical InterpretationPhysical Interpretation

Physical Interpretation

• There appears to be several indications of anisotropy

• There does not exist a model which explains all the data

Physical Interpretation

• The effect could be consistent with standard CDM model if it arises due to some unknown local effect

• Alternatively the phenomenon represents a violation of the cosmological principal

• I don’t see anything wrong with this but it would lead to a serious increase in the amount of work for theoreticians

Physical Interpretation

• There is no reason that the early universe is isotropic and homogeneous

• It might approach isotropy and homogeneity as it expands

• In this case one cannot rule out a small violation of the cosmological principle.

Violation of Lorentz Invariance

• Lorentz invariance may be violated due to quantum gravity effects (Collins et al 2004)

• The violation is found to be rather large suggesting a fine tuning problem

• The fine tuning problem is avoided if one imposes SUSY. In this case the violation is found to be of order

(MSUSY/MPL)2

(Jain and Ralston 2005)

Physical explanations for violation of isotropy

• Galactic foregrounds• Supercluster foregrounds• Anisotropic metric• Inhomogeneous metric• Spontaneous violation of isotropy• Local Rees-Sciama effect• Anisotropic cosmological constant• Anisotropic inflation, perhaps due to a vector field• Voids in our astrophysical neighbourhood• Magnetic field leading to anisotropic metric• Pseudoscalar-photon mixing in background magnetic field• Rotating universe …

Galactic Foregrounds

unknown foreground effects may explain the CMB anisotropies

This may be a good explanation if the axis lies close to the galactic plane and might explain the anisotropy at high l (Samal et al 2008) as well as the dipole modulation effect (Eriksen et al 2004)

Galactic Foregrounds

alignment of quadrupole and octopole may also arise due to Galactic foregrounds.

Removing the most contaminated part of the data removes any evidence of alignment

(Slosar and Seljak (2005))

not very surprising

Quadrupole

Octopole

Hot and cold spots lie close to galactic plane

Supercluster Foregrounds

Abramo et al (2008) argue that supercluster foregrounds in the vicinity of CMB dipole axis can explain the alignment

This can increase the quadrupole power and reduce the significance of alignment of quad and octo

The foreground might arise due to Sunyaev-Zeldovich effect due to hot electrons in the local supercluster

Local Voids

The presence of local voids at some select positions may explain the CMB anomalies

Dust filled void of radius 300 h1 Mpc, = 0.3 leads to a cold spot

T/T ~ 105

(Inoue and Silk 2008)

Inhomogeneous Universe

An inhomogeneous metric could lead to large scale CMB anisotropies. For example, it will lead to different power in different hemispheres

In this case one may also need to re-interpret the deceleration parameter (Moffat 2005)

This is also likely to produce an anisotropy in the supernova data

Spontaneous Breakdown of Isotropy Isotropy is broken locally by the gradient of a scalar field whose spatial fluctuations are dominated by long wavelength contributions

The gradient picks a particular direction and breaks isotropy locally

The long wavelength mode produces inhomogeneity which leads anisotropy in CMB

(Gordon et al 2005)

Superhorizon Mode

Erickcek et al (2008)

Inflation in Inhomogeneous Universe

Gordon (2007), Erickcek et al (2008) explain the observed hemispherical power asymmetry using this idea.

They argue that a two scalar field inflationary model can produce the required asymmetry without violating constraints on homogeneity of Universe.

Asymmetric Expansion

Berera et al (2004) obtain anisotropic expanding universe in the presence of cosmological constant and uniform background magnetic field (or strings or domain walls)

Inflation might push all but one magnetic field domain outside the horizon uniform magnetic field

Buniy et al (2006) obtain anisotropic inflationary solutions in such a universe

Anisotropic inflation with non-standard spinor

Spin half field with mass dimension 1

proposed as a dark matter candidate (Ahluwalia-Khalilova and Grumiller, 2005)

Bohmer and Mota (2008) show that inflation driven by a elko spinor is anisotropic

L

L

*

2 Elko spinor

Dipole Anisotropy in Radio Polarizations

It might arise due to propagation, provided Maxwell’s equations are suitably modified.

It can arise due to:Explicit or spontaneous violation of Lorentz invariance (Carroll et al 1990, Nodland and Ralston 1997, Andrianov et al 1998, Bassett et al 2000, Bezerra et al 2004)

Background inhomogeneous pseudoscalar (Kalb-Ramond) field (Majumdar and SenGupta, 1999) (Kar et al, 2001)

These proposals predict rotation of linear polarization independent of frequency

Pseudoscalar-photon mixing in background magnetic field predicts rotation proportional to frequency

The rotation required to explain the radio effect might conflict with the constraints from CMB B mode polarization

Alternatively the radio anisotropy might also arise due to intrinsic properties of radio galaxies in an anisotropic universe.

Large Scale Correlations of Optical Polarizations

may be explained in terms of mixing of light with hypothetical pseudoscalars in background intergalactic magnetic field

The intergalactic magnetic field is turbulent and has correlations over very large distance scales

(Agarwal, Kamal and Jain, 2009)

Questions

What constraints are imposed by CMB B modes on the different proposals?

What do these proposals predict for the high z supernova data?

Can these consistently explain all the different observations of anisotropy?

Can we propose new techniques or observations to test for isotropy and to check the earlier claims?

Summary and Conclusions

• There appear to be many indications of violation of isotropy

radio polarizations from radio galaxies optical polarizations from quasars CMB dipole, quadrupole and octopolewith a preferred axis pointing towards Virgo• We also find evidence for a dipole

modulation of power and an anomalously cold spot in CMB

Summary and Conclusions

• Other data sets

cluster peculiar velocities

distribution of galaxies

also indicate anisotropy

Summary and Conclusions

• Violation of isotropy persists even for high l CMB data

• Some of these effects may be simply due to residual foregrounds

• At high l, W band maps are found to be isotropic to a highly improbable degree. This may arise due to incorrect modeling of detector noise

Summary and Conclusions

• The physical cause of violation of isotropy is so far unknown

Thank YouThank You