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

l

igQgxd

glS

IJ

JI

s

sIJab

ss 4

1 ,

4||1STr

)2(

1 )6(2

443 0123

Myers (1999)

Nb

MaMNab XXGg 9 ..., ,1 ,0, NM 9,...,5,4, JI

3 2, 1, ,0, ba JI

s

IJIJ XXl

iQ ,

2 2

8

1

3

1

2222 )()(ˆ2K

KKi

i dxdxdxxmdxdxds

kijkij xC

3

ˆ2123

3,2,1, ji parameterize 3 out

6 dim to the D3-branes andKx denotes 3 spatial dim along

and five transverse to the D3-branes.

N

10-d IIB supergravity background

3D

PP-wave background

𝑅 4×𝐶𝑌 3

Matrix Inflation from String Theory

With9

ˆ4ˆ

222 sgm the above background with constant dilaton is solution to the SUGRA

22222

ˆ2

1,

2.3

ˆ, ,

24

1ikji

ijk

s

sjiji

s

XmXXXl

igXXXX

lV

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

9

ˆ4ˆ

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 NN

JJ 112

Tr 2

Plugging these to the action, we have:

2

23424 ˆ

2ˆ

3

2ˆ2

ˆ ˆ2

1Tr

2

m

JRM

gxdS P

ˆTr 2/1 2JDefining to make the kinetic term canonical, the potential takes the form

22

340 23

2

4)(

m

V effeff ,)1(

2

Tr ,

)1(

8

Tr

22222

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 36141018.7 eff

PMm 1082.6 6

Mass Spectrum of Spectators

(a) -modes1- )1( 2N

2eff

2eff

2, )2( 2)3)(2(

2

1mlllM l

20 Nll Degeneracy of each

l-mode is 12 l

(b) -modes 1-)1( 2N

2eff

2eff

2, )1(2)1)(2(

2

1mlllM 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

modes

1)1( 2

N

modes field-vector

13 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

m

eff

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(

l

l

2

)( 224

effg

∀𝜔 , No parametric resonance aroundthe susy-breaking vacuum

2243

22

22 ggM

a

kk 𝜑≡𝜙−𝜇

for 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

a

qXXX

•

02 A A l

2/3aX Aa 2/1 A& & tt eff 2

& td

d

'

a

a

a

a

a

2

3

4

31

3)(

2

22

2

2

2

22

a

a

a

all

al 24

1)(

2 2

22

2

2

2

22

2

)exp( lim

0

tiX

t l

l

t

ti

2

)exp( lim

0A

2

1

222

2

22

XX

n

2

2

2

22 1

2

1

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

a

Gh

ah

a

ah

a

a

a

ah

2 2

2

2

161

3 2 2

where

kk

ijijij TTS

3

jiij

crit

GW khLH

k

kd

d

kd

d

,

2

0,22

3

)(3

ln

1

ln

• 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

106

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