M-flation after BICEP2

Amjad Ashoorioon (Lancaster University)

Based onA.A, M.M. Sheikh-Jabbari, arXiv:1405.1685 [hep-th]] and A.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]

Cosmo 2014Chicago, ILAugust 25th, 2014

Mainly in collaboration withShahin Sheikh-Jabbari (IPM)

Introduction

The increasingly precise CMB measurements by Planck mission in combination with other cosmological date have ushered us into a precision early Universe cosmology era:

𝑛𝑠≡𝑑 log𝑃 𝑆

𝑑 log𝑘+1=0.9603±0.0073

𝑟 ≤0.11 ;

Planck 2013

Introduction BICEP2 surprise: claims that have observed the B-modes with at

o To embed such a model in supergravity, one has to insure the flatness of the theory on scales

Lyth (1997)

o In stringy models, due to geometric origin of inflation in higher dimensions,

McAllister & Baumann (2007)

Detection of poses theoretical model-building challenges:

Δ𝜙𝑀𝑝𝑙

≥1.06( 𝑟0.01 )

1/2

From Planck experiment: at

𝑟=0.2− 0.05+0.07

.

A priori these two experiments are not mutually-exclusive and can be reconciled

A.A., K. Dimopoulos, M.M. Sheikh-Jabbari, G. Shiu, JCAP 1402 (2014) 025, arXiv:1306.4914 A.A., K. Dimopoulos, M.M. Sheikh-Jabbari, G. Shiu, arXiv:1403.6099 [hep-th]], to appear in PLB

Realization of Large-Field Models in String Theory

Single-Field approach (aka Individualistic approach!):

Many Field approach (aka Socialistic approach!):

o An individual axionic field, whose potential is shift symmetric. in presence of fluxes spirals super-Planckian distances

Monodromy InflationSilverstein & Westphal (2008)

McAllister, Silverstein, Westphal (2009)

o Many moduli, which could be axions or not, cooperate to cause inflation.

o Even though the effective field excursion is larger than , individual field displacement is less!

N-flation, Kachru et. al (2006)M-flation, Ashoorioon & Sheikh-Jabbari (2009)Multiple M5 brane Inflation, A. Krause, M. Becker, K, Becker (2005) A. Ashoorioon & A. Krause (2006)

See Gary’s and Eva’s Talks

• 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

N D3-branes 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, one may show that there is a consistent classical truncation 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 Hill-top or Symmetry-Breaking

inflation, Linde (1992)Lyth & Boubekeur (2005)

(a)

(b)

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)

1

4105N

Analysis of the Gauged M-flation around the Single-Block Vacuum

pM610

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

𝑚χ2❑

𝐻2

𝑀𝑝𝑙2 𝑁𝑒=

𝜙 𝑓

𝜙𝑖 𝑑𝜙𝑉 (𝜙)𝑉 ′ (𝜙)

=18(𝑦−𝑥 )− 𝜇2

32ln(𝜇

2+4 𝑦𝜇2+4 𝑥 )

𝜖≡12 (𝑉

′

𝑉 )2

=1 𝑥=4𝑀𝑝𝑙2 +𝑀𝑝𝑙

❑√16𝑀𝑝𝑙2 +2𝜇2

𝑛𝑆−1=2𝜂−6𝜖|𝜙𝑖

𝑦𝑀𝑝𝑙

2 =12+√144+8 (1−𝑛𝑆 )𝜇

2/𝑀𝑝𝑙2

1−𝑛𝑆𝜂≡

𝑀𝑝𝑙2 𝑉 ′ ′

2𝑉

(1)

(2)

(3)

Solving the model parameters based on Observables

Plugging (2) and (3) in (1) one can find solve in terms of numerically.

𝐴𝑆=𝑉 (𝜙 𝑖)

24𝜋 2 𝑀𝑝𝑙4 𝜖(𝜙 𝑖)

≃2.195×10− 9One can read off

(a) Symmetry-Breaking Region

From Planck experiment, within

For and 𝑟=0.1991≃0.2 Right at the BICEP2 sweet spot

0.9457 ≤𝑛𝑆≤0.9749

However not all this interval is covered by this branch of the model!

𝑛𝑆❑𝑚𝑖𝑛=𝑛𝑆

❑𝑞𝑢𝑎𝑟𝑡𝑖𝑐 (𝑁 𝑒=60)=5861≃0.9508if

𝑛𝑆❑𝑚𝑎𝑥=𝑛𝑆

❑𝑞𝑢𝑎𝑑𝑟𝑎𝑡𝑖𝑐(𝑁 𝑒=60)=117121

≃0.9669if

0.1322≤𝑟 60≤0.2623

0.9457 ≤𝑛𝑆❑60≤0.9749

If as promised by CMBPOL

𝑟 ∈[0.1983,0 .2204 ]

(a) Symmetry-Breaking Region

Spectra of the Isocurvature modes:

o The lightest mode is gauge mode.

8.27×10− 3(𝜇→∞ )≲

For

For ¿1.24×10− 2

is the massless mode seed for dynamo mechanism that generates cosmic magnetic fields?!

Hilltop Regions (b) and (c)

From Planck experiment, within

For and 𝑟=0.0379

(when )

0.0155≤𝑟60≤0.1322

If as promised by CMBPOL 𝑟 ∈[0.0310,0 .0475]

𝜆𝑒𝑓𝑓❑ 60≲7.9948×10−14 25.43𝑀𝑝𝑙≲𝜇60

Due to symmetry at the level of background these two regions predict the same

Hilltop Regions (b) and (c) & 2/

Symmetry breaks down at the quantum level.

2/0

• In region (b), the lightest mode is gauge mode

9.83×10− 4≲• In region (c), the lightest mode is mode

2 .84×10−4≲ Around the isocurvature modes can act as preheat fields. The couplings of preheat fields to the inflaton are known.

at the peak frequency

Which can be observed at Chongqin HFGW detectoror Birmingham HFGW experiment.

Conclusions & Future Directions

• Matrix nature of the fields results in the production of isocurvature productions at the CMB scales.

• M-flation which is qualitatively new third venue within string theory inflationary model-building.

• M-flation solves the fine-tunings associated with chaotic inflation couplings.

• It produces super-Planckian effective field excursions from many individual sub-Planckian ones which yield large tensor/scalar ratio compatible with Planck.

• Due to hierarchical mass structure of the isocurvature modes, one can avoid the “beyond-the-cutoff” problem, exists in N-flation, even if

A.A., M.M. Sheikh-Jabbari, JCAP 1106 (2011) 014, arXiv:1101.0048 [hep-th]

• M-flation has a natural built-in mechanism of preheating to end inflation around the vacuum which can produces large GHz frequency gravitational wave spectrum which could be seen by ultra-high frequency gravitational probes.

• The loop corrections from interactions of the graviton with the scalar field create the term if . In M-flation and many field models such induced terms is naturally suppressed. A.A., U.Danielsson, M. M. Sheikh-Jabbari, Phys.Lett. B713 (2012) 353, arXiv:1112.2272 [hep-th]

Conclusions & Future Directions

• Open Issue I: Reheating around the

• Open Issue II: Building a full-fledged stringy setup with all moduli fixed.

Works in progress

Thank you