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:
Ξππππ
>1.06 ( π0.01 )
1/2
Embedded preheating in some regions high frequency gravitational waves.
c.f. Choudhury & Mazumdar (2013)
β’ 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 )()(Λ2K
KKi
i dxdxdxxmdxdxds
kijkij xC
3Λ2
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
π 4ΓπΆπ 3
Matrix Inflation from String TheoryWith
9Λ4Λ
222 sgm the above background with constant dilaton is solution to the SUGRA
22222
Λ21,
2.3Λ
, , 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. Λ 22Λ mm
From the brane-theory perspective, it is necessary to choose mΜ and Μ such that
9Λ4Λ
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 ,)(Λ 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 Λ
2Λ
32Λ
2Λ Μ
21Tr
2
mJRMgxdS P
ΛTr 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&
π»2
πβ2π
ππββ0.006
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,
β’ 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.
β’ 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
βπ , No parametric resonance aroundthe susy-breaking vacuum
2243
22
22 ggM
ak
k πβ‘πβπfor example for and modes:
β’ For and modes:
02 AAHA kβ’ For the gauge mode
rest masses are large aroundsusy-breakingvacuum.
Particle Creation and Preheating Scenario around SUSY Vacuum
β’ The situation is quite different around the SUSY vacuum
2
2
0
2,
effM
00
2 AM
β’ 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
β’
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
β’ Universe is transparent to GW useful source of information from early universe.
β’ This is in addition to the stochastic background of GW produced during inflation
β’ Parametric resonance could be a source of gravitational waves.
β’ 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
β’ Such GW is a probe of the inflaton potential and its couplings at the end of inflation.
β’ 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
ππ
π‘ β²
Largest j Gauge modes
ππ
π‘ β²
Largest j beta mode
β=0
β=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
Conclusionsβ’ M-flation solves the fine-tunings associated with chaotic inflation couplings and
produce super-Planckian effective field excursions during inflation.
β’ Matrix nature of the fields suggests isocurvature productions at the CMB scales.
β’ Hierarchical mass structure of the isocurvature modes, one can avoid the βbeyond-the-cutoffβ problem.
β’ 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
β’ M-flation has a natural built-in mechanism of preheating around the SUSY vacuum.
β’ Interactions of the graviton with the scalar field problem if
β’ In many-field models like M-flation, the problem can be avoided
Ξ=πππ
Ξ=πππ
π π
β’ 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.
β’ The couplings of the preheat fields are related to self couplings of inflaton, thus known.
Ashoorioon, Danielsson, Sheikh-Jabbari, Phys.Lett. B713 (2012)
β’ Other signatures in this inflationary region:
1. Observable GW at cosmological scales with
2. Iscocurvature perturbations with
Thank you
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