Report

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 ≡ + 1 = 0.9603 ± 0.0073 Planck 2013 log ≤ 0.11; Introduction BICEP2 surprise: claims that have observed the B-modes with = 0.2+0.07 −0.05 at ℓ ≃ 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 Δ 1/2 Lyth (1997) ≥ 1.06 0.01 o In stringy models, due to geometric origin of inflation in higher dimensions, Δ ≲ . McAllister & Baumann (2007) From Planck experiment: ≤ 0.11 at ∗ = 0.002 −1 , ℓ ≃ 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) Many Field approach (aka Socialistic approach!): See Gary’s and Eva’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 , 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 4 × 3 2 ˆ C 123 ij ijk x k 3 D3 PP-wave background i , j 1, 2 , 3 parameterize 3 out 6 dim to the D3-branes and 10-d IIB supergravity background ds S 2 2 dx dx g ab G MN a X M b X 8 i 1 K 1 K x denotes 3 spatial dim along and five transverse to the D3-branes. 2 i 2 2 mˆ ( x ) ( dx ) dx K dx K 4 1 d x STr 3 4 ( 2 ) l s g s 1 3 g ab N | QJ | I ig s 4 l s 2 X I ,X J C Q IJ i 2 l s 2 X IJ 0 12 3 1 4 F F Myers (1999) I , J 4 ,5 ,..., 9 M , N 0 , 1, ..., 9 IJ (6) I ,X J a , b 0 , 1, 2, 3 Matrix Inflation from String Theory 4 g s2ˆ 2 the above background with constant dilaton is solution to the SUGRA With mˆ 9 2 V 1 4 2 l s 2 2 Upon the field redefinition X ,X i i 8 g s ,X i j ig s ˆ 3 . 2 l 2 s ijk X i X j , X k 1 2 ˆ 2 X i2 m Xi ( 2 ) g s l s 3 V Tr i, 4 j X j 2 , i j i 3 ˆ g s . 8 g s k , l jkl j 2 i 2 m 2 2 2 mˆ m From the brane-theory perspective, it is necessary to choose mˆ and ˆ such that mˆ 2 2 2 4 g s ˆ 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 3 N 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 ˆ ( t ) J i , i 1, 2 , 3 J i are N dim. irreducible representation of the SU(2) algebra: J i ,J j i ijk Jk Tr J i J j N 12 N 1 ij 2 Plugging these to the action, we have: S d x 4 Defining M P g R Tr J 2 Tr J V 0 ( ) eff 4 2 1/ 2 4 ˆ 2 eff 3 2 2 1 ˆ 4 2 ˆ 3 m ˆ 2 ˆ ˆ 2 2 3 2 3 Tr J 2 Tr J 2 i i 1 to make the kinetic term canonical, the potential takes the form 3 m 2 2 2 eff 2 Tr J 2 8 N ( N 1) 2 , eff Tr J 2 2 N ( N 1) 2 , Analysis of the Gauged M-flation around the Single-Block Vacuum V ( ) eff ( ) 2 4 2 2m eff 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. 1 (a) N 5 10 (c) 4 (b) 10 6 M p Mass Spectrum of Spectators (a) ( N 1) 2 - 1 -modes 1 M ,l 2 2 l M ,l Degeneracy of each l -mode is 2 l 1 eff ( l 2 )( l 3 ) 2 eff ( l 2 ) m 2 (b) ( N 1) 2 - 1 -modes 2 0l N 2 1 2 l 2 1 l N eff ( l 2 )( l 1) 2 eff ( l 1) m 2 Degeneracy of each 2 l-mode is 2 l 1 (c) 3N 2 1 vector modes M ( N 1) 2 A ,l χ2 eff Degeneracy of each l ( l 1) 2 l-mode is 2 l 1 4 1 ( N 1) 2 1 3 N 2 1 5 N 1 modes modes vector - field modes 2 2 2 Solving the model parameters based on Observables 2 = 1 ′ ≡ 2 () 1 2 2 + 4 = − − ln 2 ′() 8 32 + 4 2 =1 − 1 = 2 − 6 2 ′′ ≡ 2 2 2 = 4 + 16 + 22 2 = (1) ≡ − ≡ − (2) 2 12 + 144 + 8 1 − 2 / 1 − (3) Plugging (2) and (3) in (1) one can find solve / in terms of numerically. = ( ) ≃ 2.195 × 10−9 4 2 24 ( ) One can read off (a) Symmetry-Breaking Region For = 0.9603, and = 60 = 0.1991 ≃ 0.2 Right at the BICEP2 sweet spot From Planck experiment, within 2 0.9457 ≤ ≤ 0.9749 However not all this interval is covered by this branch of the model! if → 0, = if → ∞, = 0.9457 ≤ 60 ( = 60) = 58 ≃ 0.9508 61 ( = 60) = ≤ 0.9749 0.1322 ≤ 60 ≤ 0.2623 If = 0.0029 as promised by CMBPOL ∈ [0.1983,0.2204] 117 ≃ 0.9669 121 (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 ( → ∞) ≲ For = 0.9603, = 1.24 × 10−2 = 0, is the massless mode 1 ⊂ generates cosmic magnetic fields?! seed for dynamo mechanism that 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 2 117 0.9457 ≤ ≤ 121 ≃ 0.9669 (when → ∞) 0.0155 ≤ 60 ≤ 0.1322 60 ≲ 7.9948 × 10−14 If = 0.0029 as promised by CMBPOL 25.43 ≲ 60 ∈ [0.0310,0.0475] Hilltop Regions (b) and (c) / 2 & 0 /2 Symmetry → − breaks down at the quantum level. • In region (b), the lightest mode is = 0 gauge mode 9.83 × 10−4 ≲ ≲ 8.27 × 10−3 ( → ∞) • In region (c), the lightest mode is = 1 −mode 2.84 × 10−4 ≲ ≲ 2.91 × 10−2 ( → ∞) Around = 0, the isocurvature modes can act as preheat fields. The couplings of preheat fields to the inflaton are known. Ω ℎ2 ∝ 10−16 at 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 subPlanckian 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 Λ = 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 Λ2 2 2 , if Λ = . 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] • 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 Thank you