PPTX - COSMO 2014

Cosmo 2014
Chicago, IL
August 25th, 2014
M-flation after BICEP2
Amjad Ashoorioon (Lancaster University)
Mainly in collaboration with
Shahin Sheikh-Jabbari (IPM)
Based on
A.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]
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:
๐‘‘ log ๐‘ƒ๐‘†
๐‘›๐‘  โ‰ก
+ 1 = 0.9603 ± 0.0073
Planck 2013
๐‘‘ log ๐‘˜
๐‘Ÿ โ‰ค 0.11;
Introduction
๏ฑ BICEP2 surprise: claims that have observed the B-modes with ๐‘Ÿ = 0.2+0.07
โˆ’0.05 at
โ„“ โ‰ƒ 80.
๏ฑ Detection of ๐‘Ÿ โ‰ฅ 0.01 poses theoretical model-building challenges:
o To embed such a model in supergravity, one has to insure the flatness of the
theory on scales
ฮ”๐œ™
๐‘Ÿ 1/2
Lyth (1997)
โ‰ฅ 1.06
๐‘€๐‘๐‘™
0.01
o In stringy models, due to geometric origin of inflation in higher dimensions, ฮ”๐œ™ โ‰ฒ
๐‘€๐‘๐‘™ .
McAllister & Baumann (2007)
๏ฑ From Planck experiment: ๐‘Ÿ โ‰ค 0.11 at ๐‘˜โˆ— = 0.002 ๐‘€๐‘๐‘ โˆ’1 , โ„“ โ‰ƒ 28
๏ฑ 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
๏ฑ Single-Field approach (aka Individualistic approach!):
o An individual axionic field, whose potential is shift symmetric. in presence of fluxes
spirals super-Planckian distances
Monodromy Inflation
Silverstein & Westphal (2008)
McAllister, Silverstein, Westphal
(2009)
๏ฑ Many Field approach (aka Socialistic approach!):
See Garyโ€™s and Evaโ€™s
Talks
o Many moduli, which could be axions or not, cooperate to cause inflation.
o Even though the effective field excursion is larger than ๐‘€๐‘๐‘™ , 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)
โ€ข Gauged M-flation
N
๐‘…4 × ๐ถ๐‘Œ3
2๏ซห†
๏ฅ ijk x k
3
C๏€ซ123ij ๏€ฝ
D3
PP-wave background
i, j ๏€ฝ 1,2,3 parameterize 3 out
10-d IIB supergravity background
๏€ซ
๏€ญ
ห†
ds ๏€ฝ 2dx dx ๏€ญ m
2
3
2
๏ƒฅ (x )
i 2
i ๏€ฝ1
S๏€ฝ
8
(dx ) ๏€ซ ๏ƒฅ dxK dxK
๏€ซ 2
6 dim ๏ž
to the D3-branes and
x K denotes 3 spatial dim along
and five transverse to the D3-branes.
K ๏€ฝ1
๏ƒฆ
igs
1
1
4
I
I
J
( 6)
๏ญ๏ฎ ๏ƒถ
๏ƒง
๏ƒท๏ƒท
d
x
STr
1
๏€ญ
๏€ญ
g
|
Q
|
๏€ซ
X
,
X
C
๏€ญ
F
F
ab
J
๏ญ
๏ฎ
3 4
2
๏ƒฒ
IJ 0123
๏ƒง
(2๏ฐ ) l s g s
4๏ฐ l s
4
๏ƒจ
๏ƒธ
๏›
g ab ๏€ฝ GMN ๏‚ถ a X M ๏‚ถ b X N
๏
I , J ๏€ฝ 4,5,...,9
M , N ๏€ฝ 0, 1, ..., 9
Q
IJ
๏€ฝ๏ค
IJ
๏€ซ
i
2๏ฐ ls2
๏›X
Myers (1999)
I
,X
J
๏
a, b ๏€ฝ 0, 1, 2, 3
Matrix Inflation from String Theory
4 g s2๏ซห† 2 the above background with constant dilaton is solution to the SUGRA
With mห† ๏€ฝ
9
2
V ๏€ฝ๏€ญ
๏€จ
1
4 2๏ฐ ls2
๏€ฉ
2
Upon the field redefinition
๏ซห†
๏›X , X ๏๏›X , X ๏๏€ซ 3.ig
2๏ฐ l
s
i
๏†i ๏‚บ
j
i
j
2
s
๏ฅ ijk X i ๏›X j , X k ๏๏€ซ
1 2 2
ห† Xi
m
2
Xi
( 2๏ฐ ) 3 g s ls2
๏ƒฆ ๏ฌ
i๏ซ
m2 2 ๏ƒถ
V ๏€ฝ Tr ๏ƒง๏ƒง ๏€ญ ๏† i , ๏† j ๏† i , ๏† j ๏€ซ
๏ฅ jkl ๏›๏† k , ๏† l ๏ ๏† j ๏€ซ
๏† i ๏ƒท๏ƒท
4
3
2
๏ƒจ
๏ƒธ
๏ฌ ๏€ฝ 8๏ฐg s
๏ซ ๏€ฝ ๏ซห† g s . 8๏ฐ g s
mห† 2 ๏€ฝ m 2
๏›
๏๏›
๏
From the brane-theory perspective, it is necessary to choose mฬ‚ and ๏ซห† such that
4 g s2๏ซห† 2
2
mห† ๏€ฝ
9
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 3N 2 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:
๏†i ๏€ฝ ๏ฆห†(t ) J i ,
i ๏€ฝ 1,2,3
J i are N dim. irreducible representation of the SU(2) algebra:
๏›J , J ๏ ๏€ฝ i๏ฅ
i
j
ijk
Jk
Tr ๏€จJ i J j ๏€ฉ ๏€ฝ
๏€จ
๏€ฉ
N
N 2 ๏€ญ 1 ๏ค ij
12
Plugging these to the action, we have:
2
๏ƒฉMP
๏ƒถ๏ƒน
1
๏ฌ
2
๏ซ
m
2๏ƒฆ
๏ญ
4
3
S ๏€ฝ ๏ƒฒd x ๏€ญ g๏ƒช
R ๏€ซ Tr J ๏ƒง๏ƒง ๏€ญ ๏‚ถ ๏ญ๏ฆห† ๏‚ถ ๏ฆห† ๏€ญ ๏ฆห† ๏€ซ
๏ฆห† ๏€ญ
๏ฆห† 2 ๏ƒท๏ƒท๏ƒบ
2
3
2
๏ƒจ 2
๏ƒธ๏ƒป
๏ƒซ 2
4
๏€จ ๏€ฉ
๏€จ ๏€ฉ
3
Tr J 2 ๏‚บ ๏ƒฅ Tr J i2
i ๏€ฝ1
1/ 2
Defining ๏ฆ ๏‚บ ๏€จTr J 2 ๏€ฉ ๏ฆห† to make the kinetic term canonical, the potential takes the form
๏ฌeff
2๏ซ eff
m2 2
V0 (๏ฆ ) ๏€ฝ
๏ฆ ๏€ญ
๏ฆ ๏€ซ ๏ฆ
4
3
2
4
3
๏ฌeff ๏‚บ
2๏ฌ
8๏ฌ
๏€ฝ
,
Tr J 2 N ( N 2 ๏€ญ 1)
๏ซ eff ๏‚บ
๏ซ
Tr J
2
๏€ฝ
2๏ซ
N ( N ๏€ญ 1)
2
,
Analysis of the Gauged M-flation around the Single-Block Vacuum
V (๏ฆ ) ๏€ฝ
๏ฌeff
4
๏ฆ 2 (๏ฆ ๏€ญ ๏ญ ) 2
2m
๏ญ๏‚บ
๏ฌeff
Hill-top or Symmetry-Breaking
inflation, Linde (1992)
Lyth & Boubekeur (2005)
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.
๏ฌ ๏‚ป1
(a)
N ๏‚ป 5๏‚ด104
(c)
(b)
๏„๏ฆ ๏‚ฃ 10๏€ญ6 M p
Mass Spectrum of ๏ฃ Spectators
l ๏ƒŽ๏š 0 ๏‚ฃ l ๏‚ฃ N ๏€ญ 2
(a) ( N ๏€ญ 1) 2 - 1 ๏ก -modes
2
M ๏ก ,l
1
๏€ฝ ๏ฌeff (l ๏€ซ 2)(l ๏€ซ 3)๏ฆ 2 ๏€ญ 2๏ซ eff (l ๏€ซ 2) ๏€ซ m 2
2
l ๏ƒŽ๏š 1๏‚ฃ l ๏‚ฃ N
(b) ( N ๏€ซ 1) 2 - 1 ๏ข -modes
2
M ๏ข ,l
1
๏€ฝ ๏ฌeff (l ๏€ญ 2)(l ๏€ญ 1)๏ฆ 2 ๏€ซ 2๏ซ eff (l ๏€ญ 1) ๏€ซ m 2
2
Degeneracy of each
l-mode is 2l ๏€ซ 1
Degeneracy of each
l-mode is 2l ๏€ซ 1
(c) 3N 2 ๏€ญ 1 vector modes
M
๏›( N ๏€ญ 1)
๏๏›
2
A ,l
๏€ฝ
๐‘šฯ‡2
๏ฌeff
4
Degeneracy of each
๏ฆ l (l ๏€ซ 1)
2
๏ ๏›
l-mode is 2l ๏€ซ 1
๏
๏€ญ 1 ๏€ซ ( N ๏€ซ 1) 2 ๏€ญ 1 ๏€ซ 3 N 2 ๏€ญ 1 ๏€ฝ 5 N ๏€ญ 1
๏ก ๏€ญ modes ๏ข ๏€ญ modes vector - field modes
2
2
๐ป2
Solving the model parameters based on Observables
2
๐‘€๐‘๐‘™
๐‘๐‘’
๐œ™๐‘–
=
1 ๐‘‰โ€ฒ
๐œ–โ‰ก
2 ๐‘‰
๐œ™๐‘“
๐‘‘๐œ™ ๐‘‰(๐œ™) 1
๐œ‡2
๐œ‡2 + 4๐‘ฆ
= ๐‘ฆโˆ’๐‘ฅ โˆ’
ln 2
๐‘‰โ€ฒ(๐œ™)
8
32
๐œ‡ + 4๐‘ฅ
2
=1
๐‘›๐‘† โˆ’ 1 = 2๐œ‚ โˆ’ 6๐œ–
๐œ™๐‘–
2 โ€ฒโ€ฒ
๐‘€๐‘๐‘™
๐‘‰
๐œ‚โ‰ก
2๐‘‰
2
2
๐‘ฅ = 4๐‘€๐‘๐‘™
+ ๐‘€๐‘๐‘™ 16๐‘€๐‘๐‘™
+ 2๐œ‡2
๐‘ฆ
2 =
๐‘€๐‘๐‘™
(1)
๐‘ฅ โ‰ก ๐œ™๐‘“ ๐œ™๐‘“ โˆ’ ๐œ‡
๐‘ฆ โ‰ก ๐œ™๐‘– ๐œ™๐‘– โˆ’ ๐œ‡
(2)
2
12 + 144 + 8 1 โˆ’ ๐‘›๐‘† ๐œ‡2 /๐‘€๐‘๐‘™
(3)
1 โˆ’ ๐‘›๐‘†
Plugging (2) and (3) in (1) one can find solve ๐œ‡/๐‘€๐‘๐‘™ in terms of ๐‘›๐‘† numerically.
๐ด๐‘† =
๐‘‰(๐œ™๐‘– )
โ‰ƒ 2.195 × 10โˆ’9
4
2
24๐œ‹ ๐‘€๐‘๐‘™ ๐œ–(๐œ™๐‘– )
One can read off ๐œ†๐‘’๐‘“๐‘“
(a) Symmetry-Breaking Region ๏ฆ ๏€พ ๏ญ
๏ฑ For ๐‘›๐‘† = 0.9603, and ๐‘๐‘’ = 60
๐‘Ÿ = 0.1991 โ‰ƒ 0.2
Right at the BICEP2
sweet spot
๏ฑ From Planck experiment, within 2๐œŽ
0.9457 โ‰ค ๐‘›๐‘† โ‰ค 0.9749
However not all this interval is covered by this branch of the model!
if ๐œ‡ โ†’ 0, ๐‘›๐‘† ๐‘š๐‘–๐‘› = ๐‘›๐‘†
๐‘ž๐‘ข๐‘Ž๐‘Ÿ๐‘ก๐‘–๐‘
if ๐œ‡ โ†’ โˆž, ๐‘›๐‘† ๐‘š๐‘Ž๐‘ฅ = ๐‘›๐‘†
0.9457 โ‰ค ๐‘›๐‘†
60
(๐‘๐‘’ = 60) =
๐‘ž๐‘ข๐‘Ž๐‘‘๐‘Ÿ๐‘Ž๐‘ก๐‘–๐‘
58
โ‰ƒ 0.9508
61
(๐‘๐‘’ = 60) =
โ‰ค 0.9749
0.1322 โ‰ค ๐‘Ÿ60 โ‰ค 0.2623
๏ฑ If ๐œŽ ๐‘›๐‘† = 0.0029 as promised by CMBPOL
๐‘Ÿ โˆˆ [0.1983,0.2204]
117
โ‰ƒ 0.9669
121
(a) Symmetry-Breaking Region ๏ฆ ๏€พ ๏ญ
๏‚ง Spectra of the Isocurvature modes:
o The lightest mode is ๐‘— = 0 gauge mode. For ๐‘๐‘’ = 60
โ‰ฒ 1.64 × 10โˆ’2 (๐œ‡ โ†’ 0)
8.27 × 10โˆ’3 (๐œ‡ โ†’ โˆž) โ‰ฒ
For ๐‘›๐‘† = 0.9603,
= 1.24 × 10โˆ’2
๐‘— = 0, is the massless mode ๐‘ˆ 1 โŠ‚ ๐‘ˆ ๐‘
generates cosmic magnetic fields?!
seed for dynamo mechanism that
Hilltop Regions (b) and (c)
๏ฆ๏€ผ๏ญ
๏ฑ Due to symmetry ๐œ™ โ†’ ๐œ™ โˆ’ ๐œ‡ at the level of background these two regions predict
the same
๏ฑ For ๐‘›๐‘† = 0.9603, and ๐‘๐‘’ = 60
๐‘Ÿ = 0.0379
๏ฑ From Planck experiment, within 2๐œŽ
117
0.9457 โ‰ค ๐‘›๐‘† โ‰ค 121 โ‰ƒ 0.9669 (when ๐œ‡ โ†’ โˆž)
0.0155 โ‰ค ๐‘Ÿ60 โ‰ค 0.1322
๐œ†๐‘’๐‘“๐‘“
60
โ‰ฒ 7.9948 × 10โˆ’14
๏ฑ If ๐œŽ ๐‘›๐‘† = 0.0029 as promised by CMBPOL
25.43 ๐‘€๐‘๐‘™ โ‰ฒ ๐œ‡60
๐‘Ÿ โˆˆ [0.0310,0.0475]
Hilltop Regions (b) and (c) ๏ญ / 2 ๏€ผ ๏ฆ ๏€ผ ๏ญ & 0 ๏€ผ ๏ฆ ๏€ผ ๏ญ / 2
๏ฑ Symmetry ๐œ™ โ†’ ๐œ™ โˆ’ ๐œ‡ breaks down at the quantum level.
โ€ข In region (b), the lightest mode is ๐‘— = 0 gauge mode
9.83 × 10โˆ’4 โ‰ฒ
โ‰ฒ 8.27 × 10โˆ’3 (๐œ‡ โ†’ โˆž)
โ€ข In region (c), the lightest mode is ๐‘— = 1 ๐›ผ โˆ’mode
2.84 × 10โˆ’4 โ‰ฒ
โ‰ฒ 2.91 × 10โˆ’2 (๐œ‡ โ†’ โˆž)
๏ฑ Around ๐œ™ = 0, the isocurvature modes can act as preheat fields. The couplings
of preheat fields to the inflaton are known.
ฮฉ๐บ๐‘Š โ„Ž2 โˆ 10โˆ’16 at the peak frequency 1 ๐บ๐ป๐‘ง
Which can be observed at Chongqin HFGW detector
or Birmingham HFGW experiment.
Conclusions & Future Directions
โ€ข M-flation solves the fine-tunings associated with chaotic inflation couplings.
โ€ข It produces super-Planckian effective field excursions from many individual subPlanckian ones which yield large tensor/scalar ratio compatible with Planck.
โ€ข M-flation which is qualitatively new third venue within string theory inflationary
model-building.
โ€ข Matrix nature of the fields results in the production of isocurvature productions at the
CMB scales.
โ€ข Due to hierarchical mass structure of the isocurvature modes, one can avoid the
๐‘€๐‘๐‘™
โ€œbeyond-the-cutoffโ€ problem, exists in N-flation, even if ฮ› = ๐‘
A.A., M.M. Sheikh-Jabbari, JCAP 1106 (2011) 014, arXiv:1101.0048 [hep-th]
Conclusions & Future Directions
โ€ข The loop corrections from interactions of the graviton with the scalar field create the
term
ฮ›2
๐‘€๐‘2
๐‘…๐œ™ 2 , if ฮ› = ๐‘€๐‘๐‘™ . 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]
โ€ข M-flation has a natural built-in mechanism of preheating to end inflation around the
๐œ™ = 0 vacuum which can produces large GHz frequency gravitational wave spectrum
which could be seen by ultra-high frequency gravitational probes.
โ€ข Open Issue I: Reheating around the ๐œ™ = ๐œ‡
โ€ข Open Issue II: Building a full-fledged stringy setup with all moduli fixed.
Works in progress
Thank you