View
55
Download
0
Category
Tags:
Preview:
DESCRIPTION
Large Primordial Non- Gaussianity from early Universe. Kazuya Koyama University of Portsmouth. Primordial curvature perturbations. Komatsu et.al. 2008. Proved by CMB anisotropies nearly scale invariant nearly adiabatic nearly Gaussian Generation mechanisms - PowerPoint PPT Presentation
Citation preview
Large Primordial Non-Gaussianity from early UniverseKazuya KoyamaUniversity of Portsmouth
•Proved by CMB anisotropies nearly scale invariant nearly adiabatic nearly Gaussian
•Generation mechanisms inflation curvaton collapsing universe (Ekpyrotic, cyclic)
Primordial curvature perturbations
0.960 0.013sn 0.16, /S
local 2NL
3( ) ( ) ( )5g gx x f x
1119 localNL
f
Komatsu et.al. 2008
Generation of curvature perturbations
•Delta N formalism curvature perturbations on superhorizon scales = fluctuations in local e-folding number
0in
( , ) ' ( ', )i
ti i
tN t x dt H t x ( , ) ( )i
BN t x N t
3( )P
Starobinsky ;85, Stewart&Sasaki ‘95
How to generate delta N
single field inflation multi-field inflation, new Ekpyroticisocurvature
curvaton,modulated reheating,multibrid inflation
adiabaticperturbations
entropyperturbations Sasaki. 2008
•Suppose delta N is caused by some field fluctuations at horizon crossing
• Bispectrum
2
,
1( , ) ...2
iI I J
I J I I J
N Nt x
1 2 3
, , ,1 2 , , , 1 2 3
, ,
( , , )
( ) ( ) perm. ( , , )I J IJI J K IJK
I I
B k k k
N N NP k P k N N N B k k k
N N
Local type (‘classical’)(local in real space=non-local in k-space)
Equilateral type (‘quantum’)(local in k-space)
31 2 3 1 2 3 1 2 3( ) ( ) ( ) 2 ( ) ( , , )Dk k k k k k B k k k
Lyth&Rodriguez ‘05
Observational constraints• local type maximum signal for
WMAP5
•Equilateral type maximum signal for
WMAP5
1k
2k 3k
1k
3k
2k
local 2NL
3( ) ( ) ( )5g gx x f x
3 1 2,k k k
1119 localNL
f
1 2 3k k k
NL
equil151 253f
Theoretical predictionsStandard inflation Non-standard scenario
Single field
K-inflation, DBI inflation
Features in potentialGhost inflation
Multifield
depending on the trajectory
DBI inflation
curvaton
new Ekpyrotic (simplest model)
isocurvature perturbations (axion CDM)
local, equil ( , ) 1NLf O equil 21 / 1NL sf c
local (1)NLf O
localNL (5 / 4) / curvaton decayf
equil 2 2(1 / ) / (1 ) 1NL s RSf c T
1( 1)localNL sf n
5 310localNLf
Rigopoulos, Shellard, van Tent ’06Wands and Vernizzi ’06Yokoyama, Suyama and Tanaka ‘07
Three examples for non-standard scenarios• (multi-field) K-inflation, DBI inflation
• (simplest) new ekpyrotic model
• (axion) CDM isocurvature model
Arroja, Mizuno, Koyama 0806.0619 JCAP
Koyama, Mizuno, Vernizzi, Wands 0708.4321 JCAP
Hikage, Koyama, Matsubara, Takahashi, Yamaguchi (hopefully) to appear soon
K-inflation•Non-canonical kinetic term
•Field perturbations (leading order in slow-roll)
4 1( , ),2
S d x gP X X
2 ,
, ,2X
sX XX
Pc
P XP
21 , 16T
ss pl
H PP r cc M P
sound speed
Amendariz-Picon et.al ‘99
Garriga&Mukhanov ‘99
Bispectrum
•DBI inflation
cf local-type
2
1 2 3 1 2 3 3 3 31 2 3
( , , ) ( , , ) ,P
B k k k F k k kk k k
local local 3 3 31 2 3 NL 1 2 3
3( , , ) ( )10
F k k k f k k k
1( ) 1 2 ( ) 1 ( )( )
P X f X Vf
1 2 3 2
1( , , )s
F k k kc
1k
3k
2k
1k
2k 3k
LoVerde et.al. ‘07
Aishahiha et.al. ‘04
Observational constraints• (too) large non-Gaussianity •Lyth bound
eff2
35 1108NL
s
fc
for equilateral configurations
2
2
1 6p
rM N
716 10sr c
1 4 0.04 0.013sn D3
anti-D3
inflaton
UV eff 300NLf Huston et.al ’07, Kobayashi et.al ‘08
Multi-field model
•Adiabatic and entropy decomposition adiabatic sound speed
entropy sound speed
4 1( , ),2
IJ IJ I JS d x gP X X
2( ) ( ),2
IJ J II J
bP X P X X X X X X 0 0X X
2 ,
0, ,2X
adX XX
Pc
P X P
201enc bX
s
adiabatic
entropy
Arroja, Mizuno, Koyama ’08Renaux-Petel, Steer, Langlois Tanaka‘08
•Multi-field k-inflation
•Multi-field DBI inflation
Final curvature perturbation
2 1enc
1( ) det( ( ) ) 1 ( )( )
IJ I JIJP X g f G V
f
2 2en adc c
( ) ( )IJP X P X
,H HS ss
* *RST S
Langlois&Renaux-Petel’08
Renaux-Petel, Steer, Langlois Tanaka‘08
Transfer from entropy mode•Tensor to scalar ratio
•Bispectrum k-dependence is the same as single field case!
large transfer from entropy mode eases constraints
•Trispectrum different k-dependence from single field case?
RST
2
1161s RS
r cT
eff2 2
35 1 1108 1NL
s RS
fc T
3eff
22,NLf
2 2
3 2
1
1
RS
RS
T
T
Mizuno, Koyama, Arroja ’09
Renaux-Petel, Steer, Langlois Tanaka‘08
New ekpyrotic models•Collapsing universe
•Ekpyrotic collapse
1H
ak
t t bounce
( ) ( ) , 1na t t n Khoury et.al. ‘01
•Old ekpyrotic model
spectrum index for is the bounce may be able to creat a scale invariant spectrum but
it depends on physics at singularity
•New ekpyrotic model
0cV V e
22/( ) ( ) ca t t
3sn
1 1 2 21 2
c cV V e V e
212/( ) ( ) ca t t
222/( ) ( ) ca t t
22/( ) ( ) ca t t
22/2 2 2
1 2
1 1 1( ) ( ) ,ca t tc c c
Khoury et.al. ‘01
Lyth ‘03
Lehners et.al , Buchbinder et.al. ‘07
B
B2
•Multi-field scaling solution is unstable entropy perturbation which has a scale invariant spectrum is converted to adiabatic perturbations
2
2 20
c Hs
1
22 2 2
1 22
T
sc H
c c
B
B
B2
B: B2:
ss
B2
Koyama, Mizuno & Wands’ 07
•Delta-N formalism
22
2
12
dN d NN s sds ds
sB
B2
s
logN a
log HN
B
B2
•Predictions
•Generalizations changing potentials conversion to adiabatic perturbations in kinetic
domination
2 21 2
local 2 1NL 1
1 11 4 0
05 5 ( 1)
12 3
s
s
nc c
r
f c n
Koyama, Mizuno, Vernizzi & Wands’ 07
Buchbinder et.al 07
Lehners &Steinhardt ‘08
Non-Gaussianity from isocurvature perturbations
• (CDM) Isocurvature perturbations are subdominant
•Non-Gaussianity can be large
0.067 ( 1)
0.008 ( 1.5) <0.001 ( 2)
SS
S
S
S
P nP P
nn
Boubekeur& Lyth ‘06, Kawasaki et.al ’08, Langlois et.al ‘08
Axion CDM•Massive scalar fields without mean
•Entropy perturbations
•Dominant nG may come from isocurvature perturbations
2 2CDM m
2 234
CDM rg g
CDM r
S
3
3/22(1)
SO
S
32
3 3eff 52
2 1/22 2
1 10NL
Sf
Linde&Mukhanov ‘97, Peebles ’98, Kawasaki et.al‘08
Bispectrum of CMB from the isocurvature perturbation
Adiabatic (fNL=10)
Equilateral triangle
SN
2
Il1l2l32 bl1l2l3
2
Cl1Cl2Cl3
l1l2l32l1l2l3
Noise: WMAP 5-year
The isocurvature perturbations can generate large non-Gaussianity (fNL~40)
adi iso
S SN N
3/2eff 41
0.067NLf
•Minkowski functional measures the topology of CMB map (=weighted some of bispectrum)
no detection of non-G from isocurvature perturbations and get constraints
comparable to constraints from power spectrum
WMAP5 constraints -Minkowski functional
0.070 ( 1)
0.042 ( 1.5)
0.0064 ( 2)
n
n
n
Hikage, Koyama, Matsubara, Takahashi, Yamaguchi ‘08
Theoretical predictionsStandard inflation Non-standard scenario
Single field
K-inflation, DBI inflation
Features in potentialGhost inflation
Multifield
depending on the trajectory
DBI inflation
curvaton
new Ekpyrotic (simplest model)
isocurvature perturbations (axion CDM)
local, equil ( , ) 1NLf O equil 21 / 1NL sf c
local (1)NLf O
localNL (5 / 4) / curvaton decayf
1( 1)localNL sf n
5 310localNLf
equil 2 2(1 / ) / (1 ) 1NL s RSf c T
Conclusions•Power spectrum from pre-WMAP to post-WMAP
•bispectrum WMAP 8year Planck
Do everything you can now!
Axion CDM
Classical mean of axion quantum fluctuations if
a aa f
inf / 2a af H
2inf / 2a H
2
inf*
*
,2
a
a
a Haa
cdm
0.82 22 *
12 11 2cdm
,
0.111.8 1010 GeV 10 GeV
a a
a
a
S r r
F arh
Recommended