Download - Tarun Souradeep

Tarun SouradeepI.U.C.A.A, Pune, India

1st Asian Winter School

Pheonix Park, Korea

(Jan 17, 2007)

Cosmology: Cosmology: towards ‘observing’ towards ‘observing’

the early universethe early universe

NASA/WMAP science team

Total energy density

Baryonic matter density

Dawn of Precision cosmology !!

Dark energy density

Good old Cosmology, … New trend !

Planck Surveyor SatelliteEuropean Space Agency: Launch 2008

CMB Task force report 2005

Near future : High resolution Cl (SPT)Near future : High resolution Cl (SPT)

Who ordered Dark Energy?

Is it the Cosmological constant?

Interestingly enough, current cosmological observations are

consistent with it being the term ‘blunder’ in GR!!!

Number count of clusters vs. redshift (dN/dz)

Near future : SZ Cluster surveys (SPT,ACT)Near future : SZ Cluster surveys (SPT,ACT)


0H

DM

b

tot

Mildly Perturbed universe at z=1100

Present universe at z=0

Gravitational Instability

Cosmic matter content

SLOAN DIGITAL SKY SURVEY (SDSS)

Few Gpc.

Present distribution of matterPresent distribution of matter

One little telltale bump !! A small excess in correlation at 150

Mpc.!

SDSS survey(astro-ph/0501171)

150 Mpc.

(Einsentein et al. 2005)

1 2( ) ( ) ( )r r r

2-po

int c

orre

lati

on o

f de

nsi

ty c

ontr

ast

Acoustic Baryon oscillations in the matter correlation function !!

Acoustic Baryon oscillations in the matter correlation function !!

The same CMB oscillations at

low redshifts !!!

SDSS survey(astro-ph/0501171)

Undeniable proof ofGravitational instability mechanism

for structure formation (from adiabatic initial perturbations) !!!

150 Mpc.

(Einsentein et al. 2005)

105 h-1 ¼ 150

Ripples in the different constituents Ripples in the different constituents

What’s the

next

frontier ?

Thompson scattering at redshift z=1100 (surface of last scattering)

generates a linear polarization pattern in the CMB sky.

Two polarization modes E&B

Four CMB spectra : ClTT, Cl

EE,ClBB,Cl

TE

• 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.

CMB Polarization

Thompson scattering of the CMB anisotropy quadrupole at the surface of last scattering generates a linear polarization pattern in the CMB.

(Fig:Hu & White , 97)

E modes

(Gradient)

B modes

(Curl)

Polarization: E modes and B modesE 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 provideimportant evidence for, and determine the energy scale of Inflation

E

B

NASA/WMAP science team 2006

(Boomerang 2003, WMAP-3)

Out of phase location of peaks in EE, TE relative to TT implies

adiabatic initial perturbations !!!

Proof of inflation !

Null BB: Awaiting direct signature of tensor

perturbations, a.k.a. cosmic

gravity waves !!!

Current status of CMB Spectra


Timeline of CMB experimentsWMAP-1yr

nowWMAP-3yr

WMAP-8yrPlanck (ESA)

Next Gen. spaceCMBPOL

Quantum fluctuations

super adiabatic amplified by

inflation (rapid expansio

n)

Galaxy & Large sc

ale

Structure fo

rmation

Via gravitational insta

bility

Early Universe

Present Universe

The Cosmic screen

Who pinged the Cosmic drum ? Who pinged the Cosmic drum ?

String theory Landscape:

Non trivial skiing slopes

A scalar field displaced from the minima of its potential

03 VH

VH 22

123

Vp 22

1

Linde’s chaotic inflation

A scalar field displaced from the minima of its potential

)(

3)3(

2

3

:onDecelerati

2

2

Vp

aH

aq

1/

Inflation2 V

time

Hu

bb

le

Rad

ius

A phase of rapid expansion in the scale factor of the universe

2

2

2

2

2

22

2

ln4

ln21

ln

ln421

parameters rollSlow

d

Hd

m

ad

d

H

d

Hd

mH

P

P

(Souradeep, Thesis 1995)

Generation of fluctuations

H2

1

2)( : fluc. q. DeSitter""

HtHN

e

dt H N : folds-e of No.

H

atxNrhHrh

|)(ln),(

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

exitreenteraHk

H

p

aHkarh

)(

,|)(ln :potentialBardeen

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

Adiabatic scalar perturbations

Reconstructing the inflaton potential from the primordial power spectrum

Energy scale and Model of inflation

(Souradeep & Sahni, 1992, Souradeep, Ph.D.thesis, 1995)

COBE-DMR normalized Hubble parameter during inflation

GeV 1015inf H

2

2

2

2

2

2

2

2

2

ln4

)3)((

,

0)(

0)(

,

d

Hd

m

HH

m

a

aV

H

m

a

aV

vVkv

uVku

ahvau

P

eff

Teff

S

kTk

kSk

kkkk

Scalar & Tensor perturbations

(Fig:Souradeep, Thesis 1995)

Power spectra of perturbations

T

s

khk

kP

kkk

kP

kT

kk

232

23

232

23

2

23

2)(

42)(

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

2

22222 )

2

1(,

12

3,

H

mk

kh

effTTS

aHkk

TaHk

k

s

T

Scale Invariant perturbation spectra

Ideal case: Never exactly possible for inflation!!

Requires

No end to dS phase

0

Pmeff 0 and 0 2

Scale free perturbation spectra

AeVd

Hd

meff

)(0ln

00

2

2

2

Very specific model : Power law inflation

Scalar & tensor spectra have the same shape

Relative amplitude and spectral index determined by

Power spectrum‘Nearly’ Scale invariant /scale free form

( … but are there features ?)

Spin characteristics Scalar --- Density perturbations

Tensor --- Gravity waves

Type of scalar perturbations Adiabatic --- no entropy fluctuations

Isocurvature -- no curvature fluctuations

Underlying statistics Gaussian

Non-Gaussian

The nature of initial/primordial perturbations

The Background universe Homogeneous & isotropic: Cosmological principle

Flat (Euclidean) Geometry ( but topology ? )

Detecting the relic

GW background : Energy scale of

inflation

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 scalarratio in the CMB


COBE

WMAP

WMAP+SDSS

Courtesy: A. Coorey (EPIC)

10-3 : reasonable low end of inflationary

possibilities

Cosmic Gravity wave background from inflation

First COBE-DMR normalized prediction of inflationary GW background spectrum

(GW energy density per log interval in wavenumber)


Cosmic Gravity wave background from inflation


Coveted Goal

Measuring the primordial power

spectrum: Features as signatures

of new physics

Primordial spectra with features

3422)( mV

Dynamics of slow roll parameters

2

2

)32)((

)(2

H

m

H

H

eff

(Souradeep, Thesis 1995)

Breaking Scale Invariance of spectra

Two distinct approaches:

1. Vary H during inflation

Changes both scalar & tensor spectra

2. Vary effective mass

Changes only scalar spectra

(Zelnikov & Mukhanov)

Breaking Scale Invariance of spectraResponse to `delta function’ effective mass : (Starobinsky 1992)

Transfer function on the scalar spectra

)(V)(V

2

2

2

2

d

Vd

H

meff

(Memari, TS 2003)

CMB anisotropy has two independent aspects:

( ) ( )l P kdk

C Gk

k

( )P k ( )lG kPost recombination Radiation transport in a given cosmology

Primordial power spectrum from Early universe

*Assume model initial power spectrum

+

* CMB anisotropy data

Cosmological parameters +

Power spectrum

Initial power spectrum

* CMB anisotropy data

+

* Cosmological parameters.

Forward (model comparsion):

Reverse (direct deconvolution):

Determining P(k)

(Kogo et al. ‘03, ’04, Matsumiya et al. ’02, Tegmark & Zaldariagga 97, ..)

(Shafieloo & Souradeep, 2004 PRD )

Recovered spectrum shows an infra-red cut-off on Horizon scale !!!

Is it QG physics ? cosmic topology ? Signature of pre-inflationary phase ? String cosmology ? ….

Primordial power spectrum from WMAPPrimordial power spectrum from WMAP

Horizon scale

Cited in WMAP-3 paper

Wavelet Decomposition of features(TS+ Rangarajan, Panigrahi, Manimaran: astro-ph/0611352 )

(AS,TS+ Rangarajan, Panigrahi, Manimaran: astro-ph/0611352 )Wavelet Decomposition of features

Recovery of the primordial power spectrum Recovery of the primordial power spectrum

(Tocchini-Vaentini, Hoffman, Silk astro-ph/0509478)

A reconfirmation of our results using different deconvolution method !

The Grand program :

( )

( )

( )

( )

( )

( )

( ) ( )

TT TT

EE

B

EE

B B

T

B

ETE

dkC

kdk

Ck

dkC

G k

G k

G k

P k

P k

P

G k

k

P k

kdk

Ck

( ), ( ), ( )S T isoP k P k P k ( ), ( ), ( ), ( )TT EE BB TEG k G k G k G k

Primordial power spectra from Early universe

Post recombination Radiative transport kernels in a given cosmology

Beyond Cl : Measuring correlation patterns in

CMB(BiPS: Bipolar power

spectra)

Statistical properties are not invariant under rotation of the sky

Breakdown of the cosmological principle ?

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 (l=2,3 aligned), 2006Copi et al. 2004 (multipole vectors), … ,2006Land & 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

.

.

Anisotropic, rotating cosmos

(Bianchi VIIh)

Cosmic topology

(Poincare Dodecahedron)

‘Anomalies’ in the WMAP CMB maps

Can we measure correlation patterns?

the COSMIC CATCH is

Beautiful Correlation patterns could underlie the CMB tapestry

Figs. J. Levin

1 2 1 2 1 2

2 1

4ˆ ˆ ˆ ˆ ˆ ˆ( , ) ( ) ( )

l

lC n n C n n P n nlC

1 2 1 2ˆ ˆ ˆ ˆ( , ) ( ) ( )C n n T n T n

T(n) : smooth Gaussian random function on a sphere (sky map), i.e., Completely specified by the two-point correlation

Advanced Statistics of CMB

Statistical isotropy implies Cl is sufficient

1 2 1 2

1 2

1 2

1 2 1 2

{ ( ) ( )}

( , ) ( )LMl l l l LM

l l LM

A Y n Y n

C n n C n n

Most general,

Bipolar Spherical HarmonicExpansion

0||21

21,,

2 llM

MllABiPS:BiPS:

rotationally invariantrotationally invariant

M

mmMlml

Mll mMlml

CaaA

1211

1

121121

*

BiPoSH BiPoSH coefficients :coefficients :

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

Recall: Coupling of angular momentum states

Mmlml |2211 0, 21121 Mmmlll

Statistical IsotropyStatistical Isotropy

0

0

Bipolar spherical

harmonics

Spherical Harmonic coefficents

BiPoSH coefficents

Angular power spectrum

BiPS

lma MllA

'

lC

Spherical harmonics

Bipolar Power spectrum (BiPS) :Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical AnisotropyA Generic Measure of Statistical Anisotropy

Bipolar spherical

harmonics

Spherical Harmonic Transforms

BipoSH Transforms


BiPS(Bipolar Power

Spectrum)

lma MllA

'

lC

Spherical harmonics

Bipolar Power spectrum (BiPS) :Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical AnisotropyA Generic Measure of Statistical Anisotropy

Bipolar spherical

harmonics

Spherical Harmonic Transforms

BipoSH Transforms


BiPS

lma MllA

'

lC

Spherical harmonics

Statistical IsotropyStatistical Isotropyi.e., NO Patternsi.e., NO Patterns 0

0

Statistical Isotropy of CMB Statistical Isotropy of CMB AnisotropyAnisotropy

W(l

)

WMAP CMB anisotropy map

WMAP Angular power spectrum

WMAP Bipolar power spectrum (BiPS)

Fig: NASA/WMAP science team

Fig: NASA/WMAP science team

Amir Hajian thesis 2006

BiPS: Spectroscopy of Cosmic topology BiPS: Spectroscopy of Cosmic topology

(Amir Hajian, Himan Mukhopadhyay, TS )(Amir Hajian, Himan Mukhopadhyay, TS )

Differentiate Cosmic vs.Differentiate Cosmic vs.

Galactic B-mode polarizationGalactic B-mode polarization

Hajian & Souradeep ApJ. Lett 2003, Hajian, Souradeep & Cornish ApJ. Lett. 2005,…

Simple Torus (Euclidean)

Compact hyperbolic space

Poincare dodecahedron

Is the Universe Compact ? Is the Universe Compact ?

Recent Nature article

Quantum creation of a

finite universe !?!

BiPS signature of a “soccer ball” universe

(Hajian, Pogosyan, TS, Contaldi, Bond : in progress.)

K

Ideal, noise free maps predictions

Poincare dodecahedron

BiPS signature of a “soccer ball” universe


013.1tot

Ideal, noise free maps predictions

Measured BiPS for a “soccer ball” universe


013.1tot

0.5

2.5

2.0

1.0

1.51000 simulated full

sky maps with WMAP noise

BiPS signature of Flat Torus spaces

Hajian & Souradeep (astro-ph/0301590)

Tuhin Ghosh, Amir Hajian & Tarun Souradeep(astro-ph/0604279)

Hunting Correlation Hunting Correlation patterns in the patterns in the

CMB AnisotropyCMB Anisotropy

Is there a hidden pattern?Jaffe et al. 2005

WMAP first year data

Rotating Universe Template

Subtraction of above two maps

BiPS of random CMB maps plus Bianchi pattern

(Tuhin Ghosh, Hajian, Souradeep, astro-ph/0604279)

Null BiPS Probability for Bianchi VIIh ( =0.5)

99.9% CL

68% CL

99% CL

(Tuhin Ghosh, Amir Hajian, Souradeep, astro-ph/0604279)

90% CL

10

0

2.55 10 at 99.9%CLH

Ultra Large scale structure of the universe

How Big is the Observable Universe ?

Relative to the local curvature & topological scales

Thank Thank you !!!you !!!