Post on 23-Feb-2016
description
Preheating in Gauged M-flation around the Supersymmetric Vacuum and its Gravitational Wave Signatures
Amjad Ashoorioon (Lancaster University)Based on a work in progress andA.A., H. Firouzjahi, M.M. Sheikh-Jabbari JCAP 0906:018,2009, arXiv:0903.1481 [hep-th],A.A., H. Firouzjahi, M.M. Sheikh-Jabbari JCAP 1005 (2010) 002, arXiv:0911.4284 [hep-th]A.A., M.M. Sheikh-Jabbari, JCAP 1106 (2011) 014, arXiv:1101.0048 [hep-th]A.A., U.Danielsson, M. M. Sheikh-Jabbari, Phys.Lett. B713 (2012) 353, arXiv:1112.2272 [hep-th]
Liverpool half a day meetingOctober 23rd, 2013
In collaboration withBrandon Fung (Waterloo)Robert B. Mann (Waterloo)Marius Oltean (McGill)Shahin Sheikh-Jabbari (IPM)
Introduction Planck data strongly supports the idea of inflation
o To embed such a model in supergravity, one has to insure the flatness of the theory on scales Lyth (1997)
o In supergravity and stringy, one usually finds the size of the region in which inflation can happen to be much smaller than plM
McAllister & Baumann (2007)
I focus on M-flation that uses Matrices as inflaton.
which puts some favourite models like in trouble, considering Bunch-Davies vacuum. c.f. Ashoorioon, Dimopoulos, Sheikh-Jabbari & Shiu (2013)
Still any detection of poses theoretical model-building challenges:
Δ𝜙𝑀𝑝𝑙
>1.06 ( 𝑟0.01 )
1/2
Embedded preheating in some regions high frequency gravitational waves.
c.f. Choudhury & Mazumdar (2013)
• Gauged M-flation
FFCXX
ligQgxd
glS
IJ
JI
s
sIJab
ss 41 ,
4||1STr
)2(1 )6(
24
43 0123Myers (1999)
Nb
MaMNab XXGg 9 ..., ,1 ,0, NM 9,...,5,4, JI
3 2, 1, ,0, ba JI
s
IJIJ XXliQ , 2 2
8
1
3
1
2222 )()(ˆ2K
KKi
i dxdxdxxmdxdxds
kijkij xC
3ˆ2
123
3,2,1, ji parameterize 3 out6 dim to the D3-branes and
Kx denotes 3 spatial dim alongand five transverse to the D3-branes.
N
10-d IIB supergravity background
3D
PP-wave background
𝑅 4×𝐶𝑌 3
Matrix Inflation from String TheoryWith
9ˆ4ˆ
222 sgm the above background with constant dilaton is solution to the SUGRA
22222
ˆ21,
2.3ˆ
, , 24
1ikji
ijk
s
sjiji
s
XmXXXl
igXXXXl
V
23)2( ss
ii
lg
X
Upon the field redefinition
2
2
2 ,
3, ,
4Tr ijlkjkljiji
miV
sg 8 ss gg 8. ˆ 22ˆ mm
From the brane-theory perspective, it is necessary to choose m̂ and ̂ such that
9ˆ4ˆ
222 sgm
We have N D3-branes that are blown up into a single giant D5-brane under the influence of RR 6-form. The inflaton corresponds to the radius of this two sphere.
Truncation to the SU(2) Sector:
i are N X N matrices and therefore we have 23N scalars. It makes the analysis very
difficult
However from the specific form of the potential and since we have three i , it is possible
to show that one can consistently restrict the classical dynamics to a sector with single scalar field:
3,2,1 ,)(ˆ iJt ii
iJ are N dim. irreducible representation of the SU(2) algebra:
kijkji JiJJ , ijji NNJJ 112
Tr 2
Plugging these to the action, we have:
2
23424 ˆ
2ˆ
32ˆ
2ˆ ̂
21Tr
2
mJRMgxdS P
ˆTr 2/1 2JDefining to make the kinetic term canonical, the potential takes the form
22
340 23
24
)(
mV effeff ,)1(
2
Tr ,
)1(8
Tr 2
2222
NNJNNJ effeff
3
1
22 TrTri
iJJ
22eff )(4
)( Veff
2
m
(a) i
Hill-top or Symmetry-Breakinginflation, Linde (1992)Lyth & Boubekeur (2005)
Pi M 57.43 Pf M 07.27 PM 26
(b) i2/
Pi M 5.23 Pf M 03.35 PM 36
141091.4 eff
(a)
(b)
PMm 1007.4 6
141018.7 effPMm 1082.6 6
In the stringy picture, we have N D3-branes that are blown up into a giant D5-brane under the influence of RR 6-form.
(c)
(c) 2/0 i
1
4105N
Analysis of the Gauged M-flation around the Single-Block Vacuum
pM610
Pi M 5.12 Pf M 97. PM 36
141018.7 effPMm 1082.6 6
Mass Spectrum of Spectators
(a) -modes1- )1( 2N
2eff
2eff
2, )2( 2)3)(2(
21 mlllM l
20 Nll Degeneracy of each
l-mode is 12 l
(b) -modes 1-)1( 2N
2eff
2eff
2, )1(2)1)(2(
21 mlllM l
Nll 1 Degeneracy of each
l-mode is 12 l
(c) vector modes13 2 N
)1(4
22, llM efflA
modes
1)1( 2
N
modes1)1( 2
N
modes field-vector13 2 N 15 2 N
Degeneracy of each
l-mode is 12 l
C) Power Spectra in Symmetry-Breaking Inflation 2/0
961.0n
1l
953.0 3
2
2
6
6
meff
eff
1110
23.1
1410187.7 eff
048.0r
CMBPOL or QUIET should be able to verify this scenario.
31012.51, R
S
P
P
PM 36& 9102 P&
𝐻2
𝑚❑2𝜒
𝑛𝑇≃−0.006
Gauged M-flation
Particle Creation and Preheating Scenario around SUSY Vacuum The backreaction of the spectator modes on the inflaton dynamics can become large when 1,
• This could be the bonus of our model, as spectator modes help to drain the energy of the inflaton, since their masses change very fast.
• One can show that if inflation ends in the susy-breaking vacuum, this process is not effective to produce spectator particles through parametric resonance:
22
2, )1(
2
effM )1(4
22
llM eff
A
03 2 kH
12
k
k
)2(2
23
effg
)1()2(
ll
2)( 2
24
effg
∀𝜔 , No parametric resonance aroundthe susy-breaking vacuum
2243
22
22 ggM
ak
k 𝜑≡𝜙−𝜇for example for and modes:
• For and modes:
02 AAHA k• For the gauge mode
rest masses are large aroundsusy-breakingvacuum.
Particle Creation and Preheating Scenario around SUSY Vacuum
• The situation is quite different around the SUSY vacuum
2
2
0
2,
effM
00
2 AM
• For large values of for and modes and for all values of for the gauge modes
10
2
k
k
parametric resonance happens.
02
23
32
aqX
XX
•
02 A A l
2/3aX Aa 2/1 A& & tt eff 2
& tdd
'
aa
aa
a
23
4313)( 2
22
2
2
2
22
aa
aall
al 241)(
2 2
22
2
2
2
22
2)exp( lim
0
tiXt
l
l
t
ti
2)exp( lim
0A
21
222
2
22
XX
n
2
22
22 121
22 an
l
ll
AA
2
22 2
eff
k&
GW production from Preheating
• Universe is transparent to GW useful source of information from early universe.
• This is in addition to the stochastic background of GW produced during inflation
• Parametric resonance could be a source of gravitational waves.
• Exponential particle production for some momenta large inhomogeneities
TTijijijijij S
aGh
ah
aah
aa
aah
2 2
2
2
1613 2 2
where k
kij
ijij TTS3
jiij
crit
GW khLHk
kdd
kdd
,
2
0,22
3
)(3
ln
1ln
• Such GW is a probe of the inflaton potential and its couplings at the end of inflation.
• We used HLattice (developed by Zhiqi Huang (2007)) to compute the GW spectrum produced by individual highest j modes as the preheat field
GW production from Preheating: Single Mode
The gravitational wave fromthe gauge modes dominates over the ones from and modes.
20 40 60 80 100 120 140
10 5
0.01
10
10 4
10 7
𝑛𝑘
𝑡 ′
Largest j Gauge modes
𝑛𝑘
𝑡 ′
Largest j beta mode
ℓ=0
ℓ=0
0 5 10 15 2010 4
10
10 6
101 1
101 6
102 1
GW production from Preheating: Three largest j Gauge Mode
The signal may be seenin HFGW detectors that probe the GHz bandBirmingham HFGW detectoror INFN Genoa HFGW resonant antenna
Conclusions• M-flation solves the fine-tunings associated with chaotic inflation couplings and
produce super-Planckian effective field excursions during inflation.
• Matrix nature of the fields suggests isocurvature productions at the CMB scales.
• Hierarchical mass structure of the isocurvature modes, one can avoid the “beyond-the-cutoff” problem.
• M-flation which is qualitatively new third venue within string theory inflationary model-building using the internal matrix degrees of freedom.
A.A., M.M. Sheikh-Jabbari, JCAP 1106 (2011) 014, arXiv:1101.0048 [hep-th]
Conclusions
• M-flation has a natural built-in mechanism of preheating around the SUSY vacuum.
• Interactions of the graviton with the scalar field problem if
• In many-field models like M-flation, the problem can be avoided
Λ=𝑀𝑝𝑙
Λ=𝑀𝑝𝑙
𝑁 𝑠
• The parametric resonance produces large GHz frequency GW which could be seen by ultra-high frequency gravitational probes like Birmingham or the one at INFN, Genoa.
• The couplings of the preheat fields are related to self couplings of inflaton, thus known.
Ashoorioon, Danielsson, Sheikh-Jabbari, Phys.Lett. B713 (2012)
• Other signatures in this inflationary region:
1. Observable GW at cosmological scales with
2. Iscocurvature perturbations with
Thank you