Tarun Souradeep

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Cosmology towards observing the early
universe
1st Asian Winter School Pheonix Park, Korea (Jan
17, 2007)
Tarun Souradeep
I.U.C.A.A, Pune, India
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Good old Cosmology, New trend !
Total energy density
Dark energy density
Baryonic matter density
Dawn of Precision cosmology !!
NASA/WMAP science team
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Planck Surveyor Satellite
European Space Agency Launch 2008
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Near future High resolution Cl (SPT)
CMB Task force report 2005
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Who ordered Dark Energy?
Is it the Cosmological constant? Interestingly
enough, current cosmological observations are
consistent with it being the L term blunder in
GR!!!
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Near future SZ Cluster surveys (SPT,ACT)
CMB Task force report 2005
Number count of clusters vs. redshift (dN/dz)
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Gravitational Instability
Mildly Perturbed universe at z1100
Present universe at z0
Cosmic matter content
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Present distribution of matter
Few Gpc.
SLOAN DIGITAL SKY SURVEY (SDSS)
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One little telltale bump !!
A small excess in correlation at 150 Mpc.! SDSS
survey (astro-ph/0501171)
(Einsentein et al. 2005)
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Acoustic Baryon oscillations in the matter
correlation function !!
150 Mpc.
105 h-1 ¼ 150
2-point correlation of density contrast
The same CMB oscillations at low redshifts
!!! SDSS survey (astro-ph/0501171)
Undeniable proof of Gravitational instability
mechanism for structure formation (from
adiabatic initial perturbations) !!!
(Einsentein et al. 2005)
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Ripples in the different constituents
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Whats the next frontier ?
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CMB Polarization
Thompson scattering at redshift z1100 (surface
of last scattering) generates a linear
polarization pattern in the CMB sky.
Two polarization modes EB Four CMB spectra
ClTT, ClEE,ClBB,ClTE

• Density (scalar) perturbations generate only
  E mode polarization.
• E-mode ¼ 5 --10 ? K
• Gravitational waves generate both the modes in
  comparable amounts .
• B-mode ¼ 0.05 0.1 ? K
• B-mode measures cosmic gravity wave background.

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CMB Polarization
Thompson scattering of the CMB anisotropy
quadrupole at the surface of last scattering
generates a linear polarization pattern in the
CMB.
(FigHu White , 97)
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E modes (Gradient)
B modes (Curl)
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Polarization E modes and B modes

• E Modes
• Gradient of the polarization
• Produced by both scalar and
• tensor modes
• Have been detected
• B Modes
• Curl of the polarization
• Produced only by tensor modes ...or
  gravitational lensing ...or foregrounds
  ...or systematics
• Expected from inflation
• Have not been detected
• A detection of primordial sourced B modes would
  provide
• important evidence for, and determine the energy
  scale of
• Inflation

E
B
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WMAP map of CMB Polarization
NASA/WMAP science team 2006
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Current status of CMB Spectra
Null BB Awaiting direct signature of tensor
perturbations, a.k.a. cosmic gravity waves !!!
Out of phase location of peaks in EE, TE
relative to TT implies adiabatic initial
perturbations !!!
Proof of inflation !
(Boomerang 2003, WMAP-3)
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CMB Task force report 2005
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CMB Task force report 2005
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Timeline of CMB experiments
CMB Task force report 2005
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Who pinged the Cosmic drum ?
Early Universe
The Cosmic screen
Present Universe
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String theory Landscape Non trivial skiing
slopes
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Generic inflation model
A scalar field displaced from the minima of its
potential
Lindes chaotic inflation
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Generic inflation model
A scalar field displaced from the minima of its
potential
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Generic inflation model
A phase of rapid expansion in the scale factor
of the universe
Hubble Radius
time
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(Souradeep, Thesis 1995)
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Generation of fluctuations
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Adiabatic scalar perturbations

• The inhomogeneous scale factor on which the space
  creation rate is constant is a measure of
  adiabatic scalar perturbations

• It is equivalent to the Gauge invariant Bardeen
  potential
• on super-Hubble radius scales

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Early universe from CMB Anisotropy

• Reconstructing the inflaton potential from the
  primordial power spectrum

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Early universe from CMB Anisotropy

• Energy scale and Model of inflation

COBE-DMR normalized Hubble parameter during
inflation
(Souradeep Sahni, 1992, Souradeep, Ph.D.thesis,
1995)
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Scalar Tensor perturbations
(FigSouradeep, Thesis 1995)
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Power spectra of perturbations

• Evaluate the mode functions at freeze out values
  on super-Hubble-radius scales.

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Scale Invariant perturbation spectra
Ideal case Never exactly possible for
inflation!! Requires No end to dS phase
Scale free perturbation spectra
Very specific model Power law inflation
Scalar tensor spectra have the same
shape Relative amplitude and spectral index
determined by
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Early universe in CMB Anisotropy
The Background universe

• Homogeneous isotropic Cosmological principle
  
• Flat (Euclidean) Geometry ( but topology
  ? )

The nature of initial/primordial perturbations
Nearly Scale invariant /scale free form (
but are there features ?)

• Power spectrum

Scalar --- Density perturbations Tensor ---
Gravity waves

• Spin characteristics

Adiabatic --- no entropy fluctuations
Isocurvature -- no curvature fluctuations

• Type of scalar perturbations

Gaussian Non-Gaussian

• Underlying statistics

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Detecting the relic GW background Energy scale
of inflation
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Early universe in CMB Anisotropy

• Tensor to scalar ratio is crucial discriminant
  of EU scenarios

Scalar --- Density perturbations ? Large
scale structure in galaxy clustering Tensor ---
Gravitational waves ? Relic stochastic GW
background Vector --- rotational modes ?
Perhaps unimportant, but primordial magnetic
field
Tensor to scalar ratio in the CMB
COBE
WMAP
WMAPSDSS
(Souradeep Sahni, 1992, Souradeep, Ph.D.thesis,
1995)
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CMB Task force report 2005
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10-3 reasonable low end of inflationary
possibilities
Courtesy A. Coorey (EPIC)
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Cosmic Gravity wave background from inflation
First COBE-DMR normalized prediction of
inflationary GW background spectrum (GW energy
density per log interval in wavenumber)
(Souradeep Sahni, 1992, Souradeep, Ph.D.thesis,
1995)
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Cosmic Gravity wave background from inflation
Coveted Goal
CMB Task force report 2005
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Measuring the primordial power spectrum
Features as signatures of new physics
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Primordial spectra with features
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Dynamics of slow roll parameters
(Souradeep, Thesis 1995)
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Breaking Scale Invariance of spectra
(Zelnikov Mukhanov)
Two distinct approaches 1. Vary H during
inflation Changes both scalar tensor spectra 2.
Vary effective mass Changes only scalar spectra
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Breaking Scale Invariance of spectra
Response to delta function effective mass
(Starobinsky 1992) Transfer function on the
scalar spectra
(Memari, TS 2003)
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Breaking Scale Invariance of spectra
Response to delta function effective mass
(Starobinsky 1992) Transfer function on the
scalar spectra
(Memari, TS 2003)
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CMB anisotropy has two independent aspects
Primordial power spectrum ?
Post recombination Radiation transport in a given
cosmology
Primordial power spectrum from Early universe
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Determining P(k)
Forward (model comparsion)
Assume model initial power spectrum CMB
anisotropy data
Cosmological parameters Power spectrum
CMB anisotropy data Cosmological parameters.
Reverse (direct deconvolution)
Initial power spectrum
(Kogo et al. 03, 04, Matsumiya et al. 02,
Tegmark Zaldariagga 97, ..)
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Primordial power spectrum from WMAP
(Shafieloo Souradeep, 2004 PRD )
Cited in WMAP-3 paper
Horizon scale
Recovered spectrum shows an infra-red cut-off on
Horizon scale !!! Is it QG physics ? cosmic
topology ? Signature of pre-inflationary phase ?
String cosmology ? .
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Wavelet Decomposition of features
(TS Rangarajan, Panigrahi, Manimaran
astro-ph/0611352 )
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Wavelet Decomposition of features
(AS,TS Rangarajan, Panigrahi, Manimaran
astro-ph/0611352 )
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Recovery of the primordial power spectrum
A reconfirmation of our results using different
deconvolution method !
(Tocchini-Vaentini, Hoffman, Silk
astro-ph/0509478)
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The Grand program
Primordial power spectra ?
Post recombination Radiative transport kernels in
a given cosmology
Primordial power spectra from Early universe
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Beyond Cl Measuring correlation patterns in
CMB (BiPS Bipolar power spectra)
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Anomalies in the WMAP CMB maps
North-South asymmetry Eriksen, et al. 2004,2006
Hansen et al. 2004 (in local power) Larson
Wandelt 2004 , Park 2004 (genus
stat.) . . Special directions (Axis of
Evil) Tegmark et al. 2004 (l2,3 aligned),
2006 Copi et al. 2004 (multipole vectors),
,2006 Land Magueijo 2004 (cubic anomalies),
Prunet et al., 2004 (mode coupling) Bernui et
al. 2005 (separation histogram) Wiaux et al.
2006 Underlying patterns T.Jaffe et al.
2005,2006 . .
Statistical properties are not invariant
under rotation of the sky Breakdown of the
cosmological principle ?
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Can we measure correlation patterns?
SI violation, or ... Correlation patterns
Beautiful Correlation patterns could underlie
the CMB tapestry
Figs. J. Levin
the COSMIC CATCH is
there is only one CMB sky !
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Advanced Statistics of CMB
? T(n) smooth Gaussian random function on a
sphere (sky map), i.e., Completely specified by
the two-point correlation
Statistical isotropy implies Cl is sufficient
Most general, Bipolar Spherical
Harmonic Expansion
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Recall Coupling of angular momentum states
BiPoSH coefficients

• Complete,Independent linear combinations of
  off-diagonal correlations.

BiPSrotationally invariant
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Bipolar spherical harmonics
Spherical harmonics
Bipolar Power spectrum (BiPS) A Generic Measure
of Statistical Anisotropy
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Bipolar spherical harmonics
Spherical harmonics
Bipolar Power spectrum (BiPS) A Generic Measure
of Statistical Anisotropy
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Bipolar spherical harmonics
Spherical harmonics
Statistical Isotropyi.e., NO Patterns


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Statistical Isotropy of CMB Anisotropy
Amir Hajian thesis 2006
WMAP Angular power spectrum
WMAP CMB anisotropy map
Fig NASA/WMAP science team
Fig NASA/WMAP science team
BiPS Spectroscopy of Cosmic topology (Amir
Hajian, Himan Mukhopadhyay, TS )
W(l)
Differentiate Cosmic vs. Galactic B-mode
polarization
WMAP Bipolar power spectrum (BiPS)
Hajian Souradeep ApJ. Lett 2003, Hajian,
Souradeep Cornish ApJ. Lett. 2005,
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Is the Universe Compact ?
Simple Torus (Euclidean)
Quantum creation of a finite universe !?!
Compact hyperbolic space
Poincare dodecahedron
Recent Nature article
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BiPS signature of a soccer ball universe
(Hajian, Pogosyan, TS, Contaldi, Bond in
progress.)
Poincare dodecahedron
Ideal, noise free maps predictions
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BiPS signature of a soccer ball universe
(Hajian, Pogosyan, TS, Contaldi, Bond in
progress.)
Ideal, noise free maps predictions
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Measured BiPS for a soccer ball universe
(Hajian, Pogosyan, TS, Contaldi, Bond in
progress.)
2.5
2.0
1000 simulated full sky maps with WMAP noise
1.5
1.0
0.5
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BiPS signature of Flat Torus spaces
Hajian Souradeep (astro-ph/0301590)
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Hunting Correlation patterns in the CMB
Anisotropy
Tuhin Ghosh, Amir Hajian Tarun
Souradeep (astro-ph/0604279)
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Is there a hidden pattern?
Jaffe et al. 2005
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(Tuhin Ghosh, Hajian, Souradeep, astro-ph/0604279)
BiPS of random CMB maps plus Bianchi pattern
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Null BiPS Probability for Bianchi VIIh ( W0.5)
(Tuhin Ghosh, Amir Hajian, Souradeep,
astro-ph/0604279)
68 CL
90 CL
99 CL
99.9 CL
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Ultra Large scale structure of the universe
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Ultra Large scale structure of the universe
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Thank you !!!
How Big is the Observable Universe ?
Relative to the local curvature topological
scales