is there a preferred direction in the universe p. jain, iit kanpur there appear to be several...
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Is there a preferred direction in the UniverseIs there a preferred direction in the Universe
P. Jain, IIT Kanpur
There appear to be several indications of the existence of a preferred direction in the Universe (or a breakdown of isotropy)
Optical polarizations from distant AGNsRadio polarizations from distant AGNsLow order multipoles of CMBR
On distance scales of less than 100 Mpc the Universe is not homogeneous and isotropic
The Virgo cluster sits at the center of this disc like structure
Most galaxies in our vicinity lie in a plane (the supergalactic plane) which is approximately perpendicular to the galactic plane.
On larger distance scales the universe appears isotropic
CFA Survey 1986
CFA Survey 1986
WMAP released very high resolution data in march 2003
Total number of pixels = 512 x 512 x 12
The data is available at 5 frequencies
There is considerable contamination from foreground emissions which complicate the interpretation of data
CMBRCMBR
What does CMBR imply about the isotropy of the universe?
CMBR Probe WMAP
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
),(),(2
l
l
lmlmlmYaT
TTemperature Fluctuations about the mean
Two Point Correlation Function
Statistical isotropy implies
If we assume that T (and alm) are Gaussian random variables (with 0 mean) then all the statistical information is contained in the two point correlation function
or
*)1( lmlml aallC
TT Cross Power SpectrumTT Cross Power Spectrum
The power is low at small l (quadrupole l=2)
The probability for such a low quadrupole to occur by a random fluctuation is 5%
Oliveira-Costa et al 2003
The Octopole is not small but very planar
Surprisingly the Octopole and Quadrupole appear to be aligned with one another with the chance probability =1/62
Quadrupole
Octopole
Cleaned Map
Oliveira-Costa et al 2003
All the hot and cold spots of the Quadrupole and Octopole lie in a plane, inclined at approx 30o to galactic plane
Extraction of Preferred AxisExtraction of Preferred AxisImagine T as a wave function
Maximize the angular momentum dispersion
Oliveira-Costa et al 2003
Extraction of Preferred AxisExtraction of Preferred Axis
k = 1 …3, m = -l … l
Preferred frame ek is obtained by Singular Value Decomposition
e represent 3 orthogonal axes in space
The preferred axes is the one with largest eigenvalue
Ralston, Jain 2003
Alternatively Define
The preferred axis for both Quadrupole and Octopole points roughly in the direction (l,b) (-110o,60o) in Virgo Constellation
Hence WMAP data suggests the existence of a preferred direction (pointing towards Virgo)
We (Ralston and Jain, 2003) show that there is considerable more evidence for this preferred direction
CMBR dipole
Anisotropy in radio polarizations from distant AGNs
Two point correlations in optical polarizations from AGNs
Also point in this directionAlso point in this direction
CMBR Dipole
The dipole is assumed to arise due to the local (peculiar) motion of the milky way, arising due to local in-homogeneities
The observed dipole also points in the direction of Virgo
Physical ExplanationsPhysical Explanations
Many explanations have been proposed for the anomalous behavior of the low order harmonics
Non trivial topology (Luminet, Weeks, Riazuelo, Leboucq and Uzan, 2003)
Anisotropic Universe (Berera, Buniy and Kephart, 2003)
Sunyaev Zeldovich effect due to local supercluster (Abramo and Sodre, 2003)
Offset angle RM)
RM : Faraday Rotation Measure
= IPA (Polarization at source)
Anisotropy in Radio PolarizationsAnisotropy in Radio Polarizations
shows a Dipole ANISOTROPY
Radio Polarizations from distant AGNs show a dipole anisotropy
Birch 1982Jain, Ralston, 1999Jain, Sarala, 2003
Likelihood Analysis The Anisotropy
is significant at 1% in full (332 sources) data set and 0.06% after making a cut in RM (265 sources)
RM - <RM>| > 6 rad/m
<RM> = 6 rad/m
= polarization offset angle
Distribution of RMDistribution of RM
The cut eliminates the data near the central peak
The radio dipole axis also points towards Virgo
Jain and Ralston, 1999
Anisotropy in Extragalactic Radio PolarizationsAnisotropy in Extragalactic Radio Polarizations
beta = polarization offset angle
Using the cut |RM - <RM>| > 6 rad/m2
Anisotropy in Extragalactic Radio PolarizationsAnisotropy in Extragalactic Radio Polarizations
Using the cut |RM - <RM>| > 6 rad/m2
Galactic Coordinates
Equatorial Coordinates
Anisotropy in Extragalactic Radio PolarizationsAnisotropy in Extragalactic Radio PolarizationsA generalized (RM dependent) statistic indicates that the entire data set shows dipole anisotropy
Possible ExplanationPossible Explanation
An anisotropically distributed background pseudoscalar field of sufficiently large strength can explain the observations
To account for the RM dependence
Rotation in polarization =g ( change in the pseudoscalar field along the path
Pseudoscalar field at source
g< 10 -11 GeV-1
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
HutsemHutseméékerskers EffectEffect
Equatorial Coordinates
1<z<2.3
Statistical AnalysisStatistical Analysis• A measure of alignment is obtained by comparing
polarization angles in a local neighborhood
The polarizations at different angular positions are compared by making a parallel transport along the great circle joining the two points
•Maximizing di() with respect to gives a measure of alignment Di and the mean angle
StatisticStatistic
k, k=1…nv are the polarizations of the nv nearest neighbours of the source i
ki = contribution due to parallel transport
Statistic Jain, Narain and Sarala, 2003
We find a strong signal of redshift dependent alignment in a data sample of 213 quasars
Alignment ResultsAlignment Results
Low polarization sample (p < 2%) High redshift sample (z > 1)
The strongest signal is seen in
Significance LevelSignificance Level
Significance LevelSignificance Level
Significance LevelSignificance Level
Large redshifts (z > 1) show alignment over the entire sky
Alignment Statistic (z > 1)Alignment Statistic (z > 1)
Alignment ResultsAlignment Results
Strongest correlation is seen at low polarizations ( p < 2%) at distance scales of order Gpc
Large redshifts z > 1 show alignment over the entire sky
Jain, Narain and Sarala, 2003
Possible ExplanationPossible Explanation
Optical Alignment can also be explained by a pseudoscalar field.
As the EM wave passes through large scale magnetic field, photons (polarized parallel to transverse magnetic field) decay into pseudoscalars
The wave gets polarized perpendicular to the transverse magnetic field
But we require magnetic field on cosmologically large distance scales
Jain, Panda and Sarala, 2002
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
Preferred AxisPreferred Axis
Optical axis is the eigenvector of S with maximum eigenvalue
Alignment StatisticAlignment Statistic
Preferred axis points towards (or opposite) to Virgo
Degree of Polarization < 2%
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 coincidencesProb. for pairwise coincidences
Ralston and Jain, 2003
Concluding RemarksConcluding RemarksThere appears to be considerable evidence that there is a preferred direction in the Universe pointing towards Virgo
However the CMBR observations may also be explained in terms of some local distortion of microwave photons due to supercluster.The physical mechanism responsible for this is not known so far.
However it is not possible to attribute optical alignment to a local effect
Future observations will hopefully clarify the situation
Radio anisotropy may also arise due to some local unknown effect
Anisotropy in Extragalactic Radio PolarizationsAnisotropy in Extragalactic Radio Polarizations
sin(2) < 0 +
sin(2) > 0
Using the cut |RM - <RM>| > 6 rad/m2
Significance Level of Radio Significance Level of Radio AnisotropyAnisotropy
Radiation propagating over cosmological Radiation propagating over cosmological distances also probes isotropy of the Universedistances also probes isotropy of the Universe
CMBR
Radiation from distant AGNs
The 3-dim space appears the same in all directions and at all locations
One way to test for isotropy and homogeneity is by observing the density of matter (galaxies) in different directions and positions
)()()( 21 nnw
Angular correlation function
or 3-D correlation function
On Large scale it is assumed that Universe is Isotropic and Homogeneous
APM Survey100 degrees by 50 degrees around the South Galactic Pole Intensities scaled to the number of galaxies blue, green and red for bright, medium and faint galaxies
The APM survey has about 5 million galaxies
It gives an accurate measure of the angular two point correlation function to about 10 degrees
The results agree reasonably well with the CDM model with
Dodelson (2003)Maddox et al (1990)