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 ๐๐ ๐๐ โก + 1 = 0.9603 ± 0.0073 Planck 2013 ๐ log ๐ ๐ โค 0.11; Introduction ๏ฑ BICEP2 surprise: claims that have observed the B-modes with ๐ = 0.2+0.07 โ0.05 at โ โ 80. ๏ฑ Detection of ๐ โฅ 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 ฮ๐ ๐ 1/2 Lyth (1997) โฅ 1.06 ๐๐๐ 0.01 o In stringy models, due to geometric origin of inflation in higher dimensions, ฮ๐ โฒ ๐๐๐ . McAllister & Baumann (2007) ๏ฑ From Planck experiment: ๐ โค 0.11 at ๐โ = 0.002 ๐๐๐ โ1 , โ โ 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 Garyโs and Evaโs Talks o Many moduli, which could be axions or not, cooperate to cause inflation. o Even though the effective field excursion is larger than ๐๐๐ , 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) โข Gauged M-flation N ๐ 4 × ๐ถ๐3 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 ๏ฅ (x ) i 2 i ๏ฝ1 S๏ฝ 8 (dx ) ๏ซ ๏ฅ dxK dxK ๏ซ 2 6 dim ๏ to the D3-branes and x K denotes 3 spatial dim along and five transverse to the D3-branes. K ๏ฝ1 ๏ฆ igs 1 1 4 I I J ( 6) ๏ญ๏ฎ ๏ถ ๏ง ๏ท๏ท d x STr 1 ๏ญ ๏ญ g | Q | ๏ซ X , X C ๏ญ F F ab J ๏ญ ๏ฎ 3 4 2 ๏ฒ IJ 0123 ๏ง (2๏ฐ ) l s g s 4๏ฐ l s 4 ๏จ ๏ธ ๏ 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 ๏ฆ ๏ฌ i๏ซ m2 2 ๏ถ V ๏ฝ Tr ๏ง๏ง ๏ญ ๏ i , ๏ j ๏ i , ๏ j ๏ซ ๏ฅ jkl ๏๏ k , ๏ l ๏ ๏ j ๏ซ ๏ i ๏ท๏ท 4 3 2 ๏จ ๏ธ ๏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 ๏ฉMP ๏ถ๏น 1 ๏ฌ 2 ๏ซ m 2๏ฆ ๏ญ 4 3 S ๏ฝ ๏ฒd x ๏ญ g๏ช R ๏ซ Tr J ๏ง๏ง ๏ญ ๏ถ ๏ญ๏ฆห ๏ถ ๏ฆห ๏ญ ๏ฆห ๏ซ ๏ฆห ๏ญ ๏ฆห 2 ๏ท๏ท๏บ 2 3 2 ๏จ 2 ๏ธ๏ป ๏ซ 2 4 ๏จ ๏ฉ ๏จ ๏ฉ 3 Tr J 2 ๏บ ๏ฅ 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 ๏๏ 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 ๏๏ 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 ๐ฯ2 ๏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 ๐ป2 Solving the model parameters based on Observables 2 ๐๐๐ ๐๐ ๐๐ = 1 ๐โฒ ๐โก 2 ๐ ๐๐ ๐๐ ๐(๐) 1 ๐2 ๐2 + 4๐ฆ = ๐ฆโ๐ฅ โ ln 2 ๐โฒ(๐) 8 32 ๐ + 4๐ฅ 2 =1 ๐๐ โ 1 = 2๐ โ 6๐ ๐๐ 2 โฒโฒ ๐๐๐ ๐ ๐โก 2๐ 2 2 ๐ฅ = 4๐๐๐ + ๐๐๐ 16๐๐๐ + 2๐2 ๐ฆ 2 = ๐๐๐ (1) ๐ฅ โก ๐๐ ๐๐ โ ๐ ๐ฆ โก ๐๐ ๐๐ โ ๐ (2) 2 12 + 144 + 8 1 โ ๐๐ ๐2 /๐๐๐ (3) 1 โ ๐๐ Plugging (2) and (3) in (1) one can find solve ๐/๐๐๐ in terms of ๐๐ numerically. ๐ด๐ = ๐(๐๐ ) โ 2.195 × 10โ9 4 2 24๐ ๐๐๐ ๐(๐๐ ) One can read off ๐๐๐๐ (a) Symmetry-Breaking Region ๏ฆ ๏พ ๏ญ ๏ฑ For ๐๐ = 0.9603, and ๐๐ = 60 ๐ = 0.1991 โ 0.2 Right at the BICEP2 sweet spot ๏ฑ From Planck experiment, within 2๐ 0.9457 โค ๐๐ โค 0.9749 However not all this interval is covered by this branch of the model! if ๐ โ 0, ๐๐ ๐๐๐ = ๐๐ ๐๐ข๐๐๐ก๐๐ if ๐ โ โ, ๐๐ ๐๐๐ฅ = ๐๐ 0.9457 โค ๐๐ 60 (๐๐ = 60) = ๐๐ข๐๐๐๐๐ก๐๐ 58 โ 0.9508 61 (๐๐ = 60) = โค 0.9749 0.1322 โค ๐60 โค 0.2623 ๏ฑ If ๐ ๐๐ = 0.0029 as promised by CMBPOL ๐ โ [0.1983,0.2204] 117 โ 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 ๐๐ = 60 โฒ 1.64 × 10โ2 (๐ โ 0) 8.27 × 10โ3 (๐ โ โ) โฒ For ๐๐ = 0.9603, = 1.24 × 10โ2 ๐ = 0, is the massless mode ๐ 1 โ ๐ ๐ generates cosmic magnetic fields?! seed for dynamo mechanism that Hilltop Regions (b) and (c) ๏ฆ๏ผ๏ญ ๏ฑ Due to symmetry ๐ โ ๐ โ ๐ at the level of background these two regions predict the same ๏ฑ For ๐๐ = 0.9603, and ๐๐ = 60 ๐ = 0.0379 ๏ฑ From Planck experiment, within 2๐ 117 0.9457 โค ๐๐ โค 121 โ 0.9669 (when ๐ โ โ) 0.0155 โค ๐60 โค 0.1322 ๐๐๐๐ 60 โฒ 7.9948 × 10โ14 ๏ฑ If ๐ ๐๐ = 0.0029 as promised by CMBPOL 25.43 ๐๐๐ โฒ ๐60 ๐ โ [0.0310,0.0475] Hilltop Regions (b) and (c) ๏ญ / 2 ๏ผ ๏ฆ ๏ผ ๏ญ & 0 ๏ผ ๏ฆ ๏ผ ๏ญ / 2 ๏ฑ Symmetry ๐ โ ๐ โ ๐ breaks down at the quantum level. โข In region (b), the lightest mode is ๐ = 0 gauge mode 9.83 × 10โ4 โฒ โฒ 8.27 × 10โ3 (๐ โ โ) โข In region (c), the lightest mode is ๐ = 1 ๐ผ โmode 2.84 × 10โ4 โฒ โฒ 2.91 × 10โ2 (๐ โ โ) ๏ฑ Around ๐ = 0, the isocurvature modes can act as preheat fields. The couplings of preheat fields to the inflaton are known. ฮฉ๐บ๐ โ2 โ 10โ16 at the peak frequency 1 ๐บ๐ป๐ง Which can be observed at Chongqin HFGW detector or Birmingham HFGW experiment. Conclusions & Future Directions โข M-flation solves the fine-tunings associated with chaotic inflation couplings. โข It produces super-Planckian effective field excursions from many individual subPlanckian ones which yield large tensor/scalar ratio compatible with Planck. โข M-flation which is qualitatively new third venue within string theory inflationary model-building. โข Matrix nature of the fields results in the production of isocurvature productions at the CMB scales. โข Due to hierarchical mass structure of the isocurvature modes, one can avoid the ๐๐๐ โbeyond-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 โข The loop corrections from interactions of the graviton with the scalar field create the term ฮ2 ๐๐2 ๐ ๐ 2 , if ฮ = ๐๐๐ . 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] โข M-flation has a natural built-in mechanism of preheating to end inflation around the ๐ = 0 vacuum which can produces large GHz frequency gravitational wave spectrum which could be seen by ultra-high frequency gravitational probes. โข Open Issue I: Reheating around the ๐ = ๐ โข Open Issue II: Building a full-fledged stringy setup with all moduli fixed. Works in progress Thank you
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