Anastasia FialkovTel Aviv University

MPIK 29.10.2012

Credit: WMAP team

Based on:

AF, Itzhaki, Kovetz (JCAP 2010)

Rathaus, AF, Itzhaki (JCAP 2011)

• Inflation is a period of ~ exponential expansion.

• Simplest model:

scalar field (inflaton, φ) slowly rolls down a ~ flat potential

Initial Conditionsfor structure formation:

Quantum fluctuations → classical Comoving

scale

Comoving

Hubble

Horizon

Inflation

Time

Observable

Window

Credit: WMAP team

Image: Loeb, Scientific American 2006

X ?

Credit: WMAP team

X ?

Credit: WMAP team

1) Particle production (thermally) before and during inflation

2) From string theory: particles, domain walls, strings

3) Cosmic anomalies

• Review of relevant cosmic anomalies

• Intro: pre-inflationary point particle (PIP)

• Cosmological signature of PIP. Can we explain the anomalies?

X ?

• In large scale structure

• In the CMB

WMAP team

SDSS webpage

WMAP team

• Large scale structure surveys: Pike, Hudson 2005; Feldman, Watkins 2008; Watkins, Feldman, Hudson 2009; Lavaux, Tully, Mohayaee, Colombi 2010; ……..

• Xrays & kSZE: Kashlinsky, Atrio-Barandela, Ebeling, Edge, Kocevski 2010; …..

• Coherence scale of 100 h-1Mpc (z ≤ 0.03)

• ∼3σ inconsistent with ΛCDM

• Flow of ~ 400 km/s toward (l = 282°, b = 6°)

(Feldman et al 2010)

“COMPOSITE” compilation. Peculiar velocity surveys

All sample is moving → attractor is far (≥ 300 h-1Mpc)

Only dipole is inconsistent with ΛCDM

(Feldman et al 2010)

Schwarz, Weinhorst 2007; Antoniou, Perivolaropoulos 2010; Colin, Mohayaee, Sarkar, Shafieloo 2011; Campanelli, Cea, Fogli, Marrone2011; ……………..

• SNe probe the Hubble flow at high redshifts (z < 0.15)

• The data is ∼ 2σ inconsistent with ΛCDM at z < 0.05

• The data confirms the bulk flow at low redshifts

The cumulative dipole direction in shells of

increasing radii. Colin, Mohayaee, Sarkar,

Shafieloo 2011) Union2 compilation (557

SNe) .

(Colin et al 2010)

Nusser, Davis 2011

Turnbull, Hudson, Feldman, Hicken, Kirshner, Watkins 2011

• Two-point angular correlation function of the CMB vanishes at large angles

• This is anomalous at 99.9% level ( >3σ )

• Also in COBE data → not a systematic!

Bennett et al 2011Hinshaw et al 1996

� Octopole is planar: power is suppressed along an axis

� Quadrupole and octopole planes are aligned.

• The alignment is 99.6% (∼3σ) anomalous• Strange 95.9 % (> 2 σ) alignment with solar system features

• No systematics found

Schwartz et al 2004

• Significance 3σ• Alignment with the bulk flow 2.5σ

• Reflection through a plane

• Compare power in even and odd l+m multipoles (low l)

Score map of directions

with maximal even and odd parity

• Hemispherical power asymmetry• Low significance (~2σ)• Possible: beam asymmetry

• The cold spot• The coldest spot on the sky (-170 µK )• Significance ~2.4 σ

The cold spot

WMAP team, NASA

CMB Galaxy surveys21-cm

SDSS

SKA

Planck

IR

Inflation

Time

Observable

Window

UV

Short inflation:� Large scales (beginning of inflation)

IR

Inflation

Time

Observable

Window

UV

Short inflation:� Large scales (beginning of inflation)

� Lack of large angular correlations

( )3

2,

VP k

Vϕ

∝

Largest observable scales

Non-scale invariant P(k)

Visible Universe

Small-field Inflation

Based on:

Itzhaki, Kovetz 2007; Itzhaki 2008 & AF, Itzhaki, Kovetz 2010

• We study slow roll inflation + add-ons:• Non-dynamical massive particle (PIP)• Massless particle• Cosmic string• Domain wall

• What are the cosmological imprints?

1. PIPs exist at the beginning of inflation.

2. One PIP in the observable universe

3. Mass of PIP can be inflaton-dependent mPIP(φ).

4. PIP has a perturbative effect on cosmology.

Slow roll

3,2 PIP PIP

,2 3PL

1 1 ( )3 0

2

Vm m xH V

a V m aϕ

ϕϕ

δδϕ δϕ δϕ

ϕ ∂

+ − ∇ + + − = ∂ && &

• The action of the inflaton (φ) + PIP:

( )4φ PIP PIP

1( )

2S S d x g V d mµ

µϕ ϕ ϕ η ϕ + = − ∂ ∂ − − ∫ ∫

,3 0H Vϕϕ ϕ+ + =&& &

• EoM for δϕ:

• PIP is a perturbation → same background eom for ϕ

PIP adds a source term to the eom of δϕ

32 PIP PIP

2 3PL

1 ( )3

2

m m xH

a m a

ε δδϕ δϕ δϕ

ϕ

∂+ − ∇ = − − ∂

&& &

PIP PIP

PL2

m m

m

ελ

ϕ∂

= −∂

Suppressed term: coupling via gravity

The leading term:

direct coupling to the inflaton

λ≡

� The solution is:

32

2 3

1 ( )3

xH

a a

δδϕ δϕ δϕ λ+ − ∇ = −&& &

Homogenous

Particular Inhomogenous

Describes the random fluctuations in the inflaton field with:

( )2

k k' 3'

2

Hk k

kδϕ δϕ δ= +

k 0δϕ = PIP,k 3 32

H

k

λδϕ

π= −

Adds 1pf to the field:

PIPδϕ

δϕδϕ

• PIP is a perturbation if we can ignore it in the background EoM:

• PIP can be detected in principle:

2PIP

2'V

a

δϕ∇<< 510λ <

PIP 1δϕ

δϕδϕ= (1)Oλ =

PIP PIP

PL2

m m

m

ελ

ϕ∂

= −∂

,3 0H Vϕϕ ϕ+ + =&& &

PIPδϕ

δϕδϕ

Wayne Hu

LensedUnlensed

WMAP team

• The large scale structure

• Signature in the CMB

• Gravitational lensing

• We evolve the perturbation through the horizon in the usual way: ξ is conserved on superhorizon scales

• After inflation ends:

Hξ δϕ

ϕ= −

&0

2

3ξΦ = −

Initial conditions for structure formation

( ) ( ) ( ) ( ) ( )0 1

9, 1

10k z k T k D z zΦ = Φ +

• We use Φ(k,z) to calculate

• Gravitational redshift effects: anisotropy in the CMB, gravitational lensing etc.

( ) ( )2 , 0r r zδρρ

∝∇ Φ = Energy density profile

( ) ( )v ,r r z∝∇Φrr

Peculiar velocity field

PIP-SOURCED STRUCTURE

• Spherically symmetric giant structure

• Characteristic scale of ~100 Mpc

• Decays log-slowly with the distance

• Is an overdense region if λ>0

PROPERTIES

( ) ( )5log 100Mpc10

rrλ

Φ ≅

( ) 2233r

r

λδ ≅

( )v0.04

rc r

λ≅

Potential well

PIP-SOURCED STRUCTURE ΛCDM STRUCTURE

( ) ( )5log 100Mpc10

rrλ

Φ ≅

( ) 2233r

r

λδ ≅

( ) 1r rΦ ≅ ( ) 31r

rδ ≅

( ) 2

v 1rrc

≅

Potential well

Decays faster and on smaller

scales (< 10 Mpc)( )v

0.04r

c r

λ≅

PIP-SOURCED STRUCTURE ΛCDM STRUCTURE

( ) ( )5log 100Mpc10

rrλ

Φ ≅

( ) 2233r

r

λδ ≅

( ) 1r rΦ ≅ ( ) 31r

rδ ≅

( ) 2

v 1rrc

≅

Decays faster and on smaller

scales (< 10 Mpc)

TIP: Search for the anomalous structure which breaks statistical isotropy

( )v0.04

rc r

λ≅

• Peculiar velocity flow with slow convergence on very large scales

• Local bulk flow (at the observer)• Anisotropy in SNIa data

� Can explain the bulk flow !

Q: What would be the signature in the CMB?

Potential well

Redshift

0

Observer

~1~1000

LSS

SW ISW

CMB Lensing

• Sachs Wolfe (SW) Effect:Photons climb out the potential well at LSS. Inhomogeneous potential at LSS.

LSS

SWLSS

3

T

T

δ Φ=

E.g.: overdensity at LSS /a cold spot.

• Integrated Sachs Wolfe (ISW): Anisotropy due to decay of the potential wells.

0ISW

LSS2

Td

T

τδτ

τ∂Φ

=∂∫

E.g.: decaying overdensity / a hot spot.

• Rings in the CMB• SW-ISW cancelation.• Signature is dominated by low-multipoles / large spots on

the CMB sky.

0r

• Gravitational lensing is deflection of light by mass

• The temperature is re-mapped

• Weak lensing → we can expand the temperature

Wayne Hu

Lensed CMBUnlensed CMB

0 LSS

LSSLSS

2r r r

drr r

δψ−

= Φ∫

E. Siegel

( ) ( )T Tθ θ δψ= +∇%

2-dimensional deflection potential:

( ) ( ) ( ) ( ) ( )GLT T T T Tθ θ δψ θ θ δ θ= +∇ ∇ = +%

• Generates non-diagonal terms in the covariance (leading order) of the CMB temperature*:

(*) ΛCDM → <δψ> = 0 → Non-diagonal terms vanishes

(*) PIP → <δψ> ≠ 0 → Signal

E. Siegel

GL 0Tδ =

( ) ( )1 2 1 2 2 1l l l l l 2 1 2 1 ccl lT T C l l l C l Cδ δψ = + < > − − + % %

• Lensing preserves brightness

SIGNAL: SW, ISW, LENSING

~GAUSSIAN NOISE

0,Tδ = ' ' ', 'lm l m l ll mmT T Cδ δ δ=

• SW and ISW change <TCMB>

• Lensing modifies <TCMB TCMB >

• Temperature is a Gaussian random field• The likelihood function:

• The signal to noise:

2

02 log logS

L LN

≡ − −

( )T 1

/2

1 1exp

22 detn

L x C xCπ

− = −

Deformed distribution Original distribution

• The 1pf of the distribution is changed

• Signal to Noise:

x x b→ +

2T 1

0

Sb C b

N− =

We want to know:

The S/N in TCMB for PIP that creates the bulk flow.

0r

λ for S/N=1

λ for bulk

flow

Tune λ at each location r0 to get the observed bulk flow → λ(r0)

With λ(r0)

0r

2 SW ISW 2,0 ,0| |l l

l l

a aS

N C

+ =

∑

With λ(r0)

0r

Two possible r0 :1. Very close to us2. In the SW - ISW cancellation region

2 SW ISW 2,0 ,0| |l l

l l

a aS

N C

+ =

∑

• For an anomalous lens we can use same S/N

• Complete reconstruction of the deflection potential.

Observed:

random non-random

ΛCDMψ δψ+

E. Siegel

• Gaussian distribution →

22

IDEAL

lm

lm l

S

N Cψ

δψ =

∑

E. Siegel

2 2

OTHER IDEAL

S S

N N <

Upper limit of the S/N from lensing. Any observable S/N should be smaller!

22

IDEAL

lm

lm l

S

N Cψ

δψ =

∑

A lot of Info in Lensing (Integrated along the geodesics).

How much of it can we see on areal CMB map?

Wayne Hu

LensedUnlensed

• The covariance matrix is deformed

• S/N:

0C C→

( ) ( )2

10 0Tr 1 log det / det

SC C C C

N− = − +

Realistic S/N (Assumes Gaussian TCMB)Deformation of the Covariance

2

0 1 22C C C C

εε= + +

22 2

1

0 02

ij

ii jjij

CS

N C C

ε =

∑

• The covariance matrix is deformed

• S/N:

• Small deformation:

Realistic S/N (Assumes Gaussian TCMB)Deformation of the Covariance

0C C→

( ) ( )2

10 0Tr 1 log det / det

SC C C C

N− = − +

Lets assume Gaussian distribution for the lensed TCMB:

Where:

22, '

'TEMP '

1

2l l

T Tll l l

CS

N C C

∆ =

∑

( )( )' '' ' ccll l lC l l l C lCδψ∆ = − − +

Our Case:

• Wrong behavior at l > 2000.• Universal: No dependence on the deflecting potential & model

parameters

2

TEMP2

IDEAL

S

NS

N

• We know: LCDM weak lensing adds non-Gaussianity to TCMB via connected 4pf

(e.g. Lewis & Challinor 2006)

(e.g. Lewis & Challinor 2006)

• “Field Theory for Lensing”: Feynmann rules

Propagator: TCMB power spectrum

Vertices:LCDM 4pf (connected)

Single lens (by PIP)

• We know: LCDM weak lensing adds non-Gaussianity to TCMB via connected 4pf

• An alternative way to calculate the realistic S/N

22, '

'TEMP '

1

2l l

T Tll l l

CS

N C C

∆ =

∑ =

22, '

'TEMP '

1

2l l

T Tll l l

CS

N C C

∆ =

∑ =

• The 2-loop correction to the S/N (from the non-Gaussianity)

+2

OBS

S

N

=

• An alternative way to calculate the realistic S/N

• Substructure of the vertex is complicated

• 4 different ways to add the lens and to close loops

Positive

Negative

• Substructure of the vertex is complicated

• 4 different ways to add the lens and to close loops

( ) ( )2 2

OBS IDEAL

1

10S S

N N=

2

OBS2

IDEAL

S

NS

N

• The approximated SN2 for a realistic experiment

• The “realistic” signal to noise is high in the SW-ISW cancellation region.

2 2

OBS IDEAL

1

10

S S

N N =

• Non-gaussianity of TCMB MUST be taken into account.

• Results hold for any “single lens”, which breaks statistical isotropy

• Other examples for a single lens:• Texture (Turok & Spergel 1990)• Giant Void (Inoue & Silk 2007)

• Previous works: lensing by a giant void and a texture.

• Neither the ideal limit on detection nor the effect of non-Gaussianity considered.

( )IDEAL

3.9SN = ( )

OBS1.3S

N =

• Constrain PIP and explain lack of large angular correlations & dipole in peculiar velocity

• Future probe:21-cm

• For any single lens non-Gaussianities must not be overlooked

SW ISW

CMB Lensing

3-D Tomography