Exploring Large-Field Inflation Models in String Theory

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: ?? ?log?? ?log?+ 1 = 0.9603 0.0073 Planck 2013 ? 0.11;

Introduction BICEP2 surprise: claims that have observed the B-modes with at +0.07 ? = 0.2 0.05 80. Detection of ? 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 ? ??? 1/2 ? Lyth (1997) 1.06 0.01 o In stringy models, due to geometric origin of inflation in higher dimensions, ? ???. McAllister & Baumann (2007) From Planck experiment: ? 0.11 at ? = 0.002 ??? 1, 28 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!): 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) See Gary s and Eva s Talks Many Field approach (aka Socialistic approach!): 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)

Gauged M-flation N 3 2 ?4 ??3 123 = + k C x ij ijk 3 D PP-wave background , = j 6 dim to the D3-branes and K x denotes 3 spatial dim along and five transverse to the D3-branes. parameterize 3 out 3 , 2 , 1 i 10-d IIB supergravity background 3 8 = i = K + + = + 2 2 2 2 i 2 ( ) ( ) ds dx dx m x dx dx dx K K 1 1 ig 1 3 1 = + I J I J 4 ) 6 ( S d x g Q X X C F F s STr 1 | | , Myers (1999) ab 4 4 2 l g l 2 ( ) 4 IJ 0123 s s s = = M N , , = b a 5 , 4 , 0 ,..., 2, 1, 9 I J , 1 , 0 = g G X X , ..., 9 M N ab MN a b 3 i = + IJ IJ I J , Q X X 2 2 l s

Matrix Inflation from String Theory 4 m = the above background with constant dilaton is solution to the SUGRA 2 2 s g With 2 9 ) l 1 1 ig = + + 2 2 i ijk , , , s V X X X X X X X m X ( i j i j i j k 2 2 s 2 . 3 2 2 s 4 2 l X Upon the field redefinition i i j 3) 2 s 2 ( g l s 2 i m 8 = + + 2 i Tr , , , V i i j jkl k l j 4 3 2 = s g 2 m = 2 = 8 g g m . s s From the brane-theory perspective, it is necessary to choose m and such that 4 m = 2 2 sg 2 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: 2 are N X N matrices and therefore we have difficult scalars. It makes the analysis very 3N i However, one may show that there is a consistent classical truncation to a sector with single scalar field: ( = 3 , 2 , 1 = ) , t J i i i i J are N dim. irreducible representation of the SU(2) algebra: ijk j i i J J = , ( ) 1 ( ) N 12 J = 2 Tr J J N k i j ij Plugging these to the action, we have: = 2 ( Tr J Defining 2 1 2 M m ( ) ( ) 3 = i + + 4 2 4 3 2 Tr P S d x g R J 2 2 Tr Tr J i J 2 2 3 2 1 ) 2 / 1 to make the kinetic term canonical, the potential takes the form 2 2 2 2 m 8 N 2 N eff eff = + = = 4 3 2 ( ) , , V eff eff 0 ) 1 2 2 J N Tr ( 4 3 2 ) 1 2 2 J N Tr (

Analysis of the Gauged M-flation around the Single-Block Vacuum m 2 Hill-top or Symmetry-Breaking inflation, Linde (1992) Lyth & Boubekeur (2005) = 2 2 ( ) ( ) eff 4 V eff 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. 1 (a) 5 4 10 N (c) (b) 10 6 M p

Mass Spectrum of Spectators (a) -modes 0 2 l l N ) 1 2 ( - 1 N Degeneracy of each l-mode is 2 + l 1 1 = + + + + 2 2 2 ( 2 )( ) 3 2 ( ) 2 M l l l m , eff eff l 2 (b) ) 1 + 1 2 l l N N ( 1 - -modes 1 l = Degeneracy of each l -mode is 2 + l 1 ) 1 + ) 1 + 2 2 2 ( 2 )( 2 ( M l l l m , eff eff 2 2 3 1 N (c) vector modes 2 ? Degeneracy of each l -mode is eff = ) 1 + 2 A 2 ( M l l 2 + l , l 1 4 = N 2 + ) 1 + ) 1 + N 2 2 2 N 5 1 ( 1 ( 1 3 1 N ?2 modes modes vector - field modes

Solving the model parameters based on Observables ???? ?(?) ? (?) 8? ? ?2 ?2+ 4? ?2+ 4? =1 ? ???? ? ? ???? ? 2??= (1) ??? 32ln ?? 2 ? ? (2) ? 1 2+ ??? 16??? 2+ 2?2 ? = 4??? = 1 2 2 144 + 8 1 ???2/??? 12 + ?? 1 = 2? 6? ? (3) 2= ?? 1 ?? ??? 2? 2 ? ? ??? Plugging (2) and (3) in (1) one can find solve ?/??? in terms of ?? numerically. ?(??) One can read off ???? 4?(??) 2.195 10 9 ??= 24?2???

(a) Symmetry-Breaking Region Right at the BICEP2 sweet spot For ??= 0.9603, and ??= 60 ? = 0.1991 0.2 From Planck experiment, within 2? 0.9457 ?? 0.9749 However not all this interval is covered by this branch of the model! ???????(??= 60) =58 if ? 0, ?????= ?? 61 0.9508 ?????????(??= 60) =117 if ? , ?????= ?? 121 0.9669 60 0.9749 0.9457 ?? 0.1322 ?60 0.2623 If ? ?? = 0.0029 as promised by CMBPOL ? [0.1983,0.2204]

(a) Symmetry-Breaking Region Spectra of the Isocurvature modes: o The lightest mode is ? = 0 gauge mode. For ??= 60 1.64 10 2(? 0) 8.27 10 3 (? ) = 1.24 10 2 For ??= 0.9603, ? = 0, is the massless mode ? 1 ? ? seed for dynamo mechanism that generates cosmic magnetic fields?!

Hilltop Regions (b) and (c) Due to symmetry ? ? ? at the level of background these two regions predict the same For ??= 0.9603, and ??= 60 ? = 0.0379 From Planck experiment, within 2? 0.9457 ?? 117 121 0.9669 (when ? ) 0.0155 ?60 0.1322 60 7.9948 10 14 25.43 ??? ?60 ???? If ? ?? = 0.0029 as promised by CMBPOL ? [0.0310,0.0475]

/ 2 0 / 2 Hilltop Regions (b) and (c) & Symmetry ? ? ? breaks down at the quantum level. In region (b), the lightest mode is ? = 0 gauge mode 8.27 10 3(? ) 9.83 10 4 In region (c), the lightest mode is ? = 1? mode 2.91 10 2(? ) 2.84 10 4 Around ? = 0, the isocurvature modes can act as preheat fields. The couplings of preheat fields to the inflaton are known. ?? 2 10 16at the peak frequency 1 ??? Which can be observed at Chongqin HFGW detector or Birmingham HFGW experiment.

Conclusions & Future Directions 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. M-flation which is qualitatively new third venue within string theory inflationary model-building. Matrix nature of the fields results in the production of isocurvature productions at the CMB scales. 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]

Conclusions & Future Directions The loop corrections from interactions of the graviton with the scalar field create the term 2 ?? naturally suppressed. A.A., U.Danielsson, M. M. Sheikh-Jabbari, Phys.Lett. B713 (2012) 353, arXiv:1112.2272 [hep-th] 2 ??2, if = ???. In M-flation and many field models such induced terms is M-flation has a natural built-in mechanism of preheating to end inflation around the ? = 0 vacuum which can produces large GHz frequency gravitational wave spectrum which could be seen by ultra-high frequency gravitational probes. Open Issue I: Reheating around the ? = ? Open Issue II: Building a full-fledged stringy setup with all moduli fixed. Works in progress

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