Liverpool half a day meeting October 23rd, 2013 Preheating in Gauged M-flation around the Supersymmetric Vacuum and its Gravitational Wave Signatures Amjad Ashoorioon (Lancaster University) In collaboration with Brandon Fung (Waterloo) Robert B. Mann (Waterloo) Marius Oltean (McGill) Shahin Sheikh-Jabbari (IPM) Based on a work in progress 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 Planck data strongly supports the idea of inflation which puts some favourite models like in trouble, considering Bunch-Davies vacuum. c.f. Ashoorioon, Dimopoulos, Sheikh-Jabbari & Shiu (2013) Still any detection of poses theoretical model-building challenges: o To embed such a model in supergravity, one has to insure the flatness of the theory on scales Lyth (1997) >1.06 0.01 1/2 ( ) c.f. Choudhury & Mazumdar (2013) o In supergravity and stringy, one usually finds the size of the region in which M pl inflation can happen to be much smaller than McAllister & Baumann (2007) I focus on M-flation that uses Matrices as inflaton. Embedded preheating in some regions high frequency gravitational waves.

Gauged M-flation N 4 3 C123ij 2 ijk x k 3 D3 PP-wave background i, j 1,2,3 parameterize 3 out 6 dim to the D3-branes and x K denotes 3 spatial dim along 10-d IIB supergravity background 2 ds 2dx dx m 2 3 i 2 (x ) i 1 S 1 4 1 d x STr (2 ) 3 l s4 g s g ab GMN a X M b X N 2

8 (dx ) dxK dxK and five transverse to the D3-branes. K 1 gab | QJI | ig s 1 ) X I , X J C (IJ60123 F F 2 4 l s 4 Q IJ IJ Myers (1999) I , J 4,5,...,9 M , N 0, 1, ..., 9 i X I,X J 2 2 ls a, b 0, 1, 2, 3 Matrix Inflation from String Theory 4 g s2 2 the above background with constant dilaton is solution to the SUGRA With m 9 2

V 1 4 2 l s2 2 Upon the field redefinition X , X X , X 3.ig 2 l i i j i j s 2 s ijk X i X j , X k 1 2 2 Xi m 2 Xi (2 ) 3 g s ls2 i m2 2 V Tr i , j i , j jkl k , l j i 4 3 2 8g s g s . 8 g s

m 2 m 2 From the brane-theory perspective, it is necessary to choose m and such that 4 g s2 2 2 m 9 We have N D3-branes that 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 from the specific form of the potential and since we have three i , it is possible to show that one can consistently restrict the classical dynamics to a sector with single scalar field: i (t ) J i , i 1,2,3 J i are N dim. irreducible representation of the SU(2) algebra: J , J i i j ijk Jk N Tr J i J j N 2 1 ij 12 Plugging these to the action, we have: 2 MP 1 2

m 2 4 3 S d x g R Tr J 2 2 3 2 2 2 4 3 Tr J 2 Tr J i2 i 1 Defining Tr J 2 to make the kinetic term canonical, the potential takes the form 1/ 2 eff 4 2 eff 3 m 2 2 V0 ( ) 4 3 2 eff 2 8 , Tr J 2 N ( N 2 1) eff Tr J 2

2 2 N ( N 1) , Analysis of the Gauged M-flation around the Single-Block Vacuum V ( ) eff 2 ( ) 2 4 2m eff Hill-top or Symmetry-Breaking inflation, Linde (1992) Lyth & Boubekeur (2005) (a) 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. (a) i (c) i 43.57 M P f 27.07 M P eff 4.9110 14 m 4.07 10 6 M P (b) 26 M P 1 (b) / 2 i i 23.5 M P eff 7.18 10 14 f 35.03 M P 36 M P

m 6.82 10 6 M P (c) 0 i / 2 i 12.5 M P eff 7.18 10 14 N 510 4 f .97 M P m 6.82 10 6 M P 36 M P 10 6 M p Mass Spectrum of Spectators (a) ( N 1) 2 - 1 -modes M 2 ,l l Degeneracy of each l -mode is 2l 1 1 eff (l 2)(l 3) 2 2 eff (l 2) m 2 2 l 1 l N (b) ( N 1) 2 - 1 -modes M 0 l N 2 2 ,l Degeneracy of each l-mode is 2l 1 1 eff (l 2)(l 1) 2 2 eff (l 1) m 2 2 (c) 3N 2 1 vector modes

Degeneracy of each M ( N 1) 2 A ,l eff 2 l (l 1) 4 l-mode is 2l 1 2 1 ( N 1) 2 1 3 N 2 1 5 N 1 modes modes vector - field modes 2 C) Power Spectra in Symmetry-Breaking Inflation 0 / 2 eff 7.187 10 14 & l 1 6eff 2 1.23 6 eff 10 11 36 M P n 0.961 & P 2 10 9 PS ,1 0.953 3 PR 2 5.12 10 3

m2 2 r 0.048 0.006 CMBPOL or QUIET should be able to verify this scenario. Gauged M-flation Particle Creation and Preheating Scenario around SUSY Vacuum The backreaction of the spectator modes on the inflaton dynamics can become large when , 1 This could be the bonus of our model, as spectator modes help to drain the energy of the inflaton, since their masses change very fast. One can show that if inflation ends in the susy-breaking vacuum, this process is not effective to produce spectator particles through parametric resonance: M 2 , eff 2 ( 1) 2 2 (l 2) (l 1) M For and modes: 3H 2k 0 For the gauge mode HA 2 A 0 A k for example for and modes: k2 2 k 2 M 2 g 3 g 42 2 a ,

k 2k 1 2 A eff 2 l (l 1) 4 eff ( 2 ) g 2 2 4 rest masses are large around susy-breaking vacuum. g3 eff ( 2 2 ) 2 No parametric resonance around the susy-breaking vacuum Particle Creation and Preheating Scenario around SUSY Vacuum The situation is quite different around the SUSY vacuum M 2 , 0 M A2 eff 2 2 0 0

For large values of for and modes and for all values of for the gauge modes k 2k X a 3 / 2 & A a1 / 2 A 2 X X 2 3 a 2 0 & t eff t 2 ' & t 0 n 2 & 2k 2 eff 2 2 2 2 2

1 a2 a ( l l ) a 2 2 2 4 a 2 2a exp( i l t ) A lim 2 l t 0 l2 exp( i t ) 2 2 X 2 2 1 X 2 2 2 d dt A l2 A 0 0 2 2 2 3 3 a2 3 a ( ) 1

a2 2 4 a2 2 a lim X 2 qX 3 parametric resonance happens. 1 n l 2 l 2 A2 1 1 2 A 2 l2 2 a2 GW production from Preheating Parametric resonance could be a source of gravitational waves. Exponential particle production for some momenta 2 a h 2 2 a h 3 a h 1 2h 16 G S TT ij ij 2 a 2 a ij a ij a ij a

dGW 1 d k3 2 2 d ln k crit d ln k 3H L large inhomogeneities S ij T ij where hij,0 (k ) ij k Tk 3 2 i, j This is in addition to the stochastic background of GW produced during inflation Such GW is a probe of the inflaton potential and its couplings at the end of inflation. Universe is transparent to GW useful source of information from early universe. GW production from Preheating: Single Mode We used HLattice (developed by Zhiqi Huang (2007)) to compute the GW spectrum produced by individual highest j modes as the preheat field The gravitational wave from the gauge modes dominates over the ones from and modes. 10 7 Largest j Gauge modes 10 4 =0 10 0 .0 1 10 5

20 40 60 80 100 120 140 1021 1016 1011 Largest j beta mode 106 =0 10 104 0 5 10 15 20 GW production from Preheating: Three largest j Gauge Mode The signal may be seen in HFGW detectors that probe the GHz band Birmingham HFGW detector or INFN Genoa HFGW resonant antenna Conclusions

M-flation solves the fine-tunings associated with chaotic inflation couplings and produce super-Planckian effective field excursions during inflation. M-flation which is qualitatively new third venue within string theory inflationary model-building using the internal matrix degrees of freedom. Matrix nature of the fields suggests isocurvature productions at the CMB scales. Hierarchical mass structure of the isocurvature modes, one can avoid the beyond-the-cutoff problem. A.A., M.M. Sheikh-Jabbari, JCAP 1106 (2011) 014, arXiv:1101.0048 [hep-th] Conclusions Interactions of the graviton with the scalar field problem if = In many-field models like M-flation, the problem can be avoided = Ashoorioon, Danielsson, Sheikh-Jabbari, Phys.Lett. B713 (2012) M-flation has a natural built-in mechanism of preheating around the SUSY vacuum. The couplings of the preheat fields are related to self couplings of inflaton, thus known. The parametric resonance produces large GHz frequency GW which could be seen by ultra-high frequency gravitational probes like Birmingham or the one at INFN, Genoa. Other signatures in this inflationary region: 1. Observable GW at cosmological scales with 2. Iscocurvature perturbations with Thank you