M- flation after BICEP2

1. Cosmo 2014 Chicago, IL August 25th, 2014 M-flation after BICEP2 AmjadAshoorioon(Lancaster University) Mainly in collaboration with ShahinSheikh-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]

2. 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: Planck 2013

3. Introduction • BICEP2 surprise: claims that have observed the B-modes with at . • Detection of poses theoretical model-building challenges: • To embed such a model in supergravity, one has to insure the flatness of the theory on scales • Lyth (1997) • In stringy models, due to geometric origin of inflation in higher dimensions, McAllister & Baumann (2007) • From Planck experiment: at • 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

4. Realization of Large-Field Models in String Theory • Single-Field approach (aka Individualistic approach!): • 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!): • Many moduli, which could be axionsor not, cooperate to cause inflation. • 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)

5. Gauged M-flation PP-wave background parameterize 3 out 6 dim to the D3-branes and 10-d IIB supergravity background denotes 3 spatial dim along and five transverse to the D3-branes. Myers (1999)

6. Matrix Inflation from String Theory the above background with constant dilaton is solution to the SUGRA With Upon the field redefinition From the brane-theory perspective, it is necessary to choose and such that ND3-branes are blown up into a singlegiant D5-brane under the influence of RR 6-form. The inflaton corresponds to the radius of this two sphere.

7. Truncation to the SU(2) Sector: are N X N matrices and therefore we have 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: are N dim. irreducible representation of the SU(2) algebra: Plugging these to the action, we have: Defining to make the kinetic term canonical, the potential takes the form

8. Analysis of the Gauged M-flation around the Single-Block Vacuum 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. (a) (c) (b)

9. Mass Spectrum of  Spectators (a) -modes Degeneracy of each -mode is (b) -modes Degeneracy of each -mode is (c) vector modes Degeneracy of each -mode is

10. Solving the model parameters based on Observables (1) (2) (3) Plugging (2) and (3) in (1) one can find solve in terms of numerically. One can read off

11. (a) Symmetry-Breaking Region Right at the BICEP2 sweet spot • For and • From Planck experiment, within However not all this interval is covered by this branch of the model! if if • If as promised by CMBPOL

12. (a) Symmetry-Breaking Region • Spectra of the Isocurvature modes: • The lightest mode is gauge mode. For For is the massless mode seed for dynamo mechanism that generates cosmic magnetic fields?!

13. Hilltop Regions (b) and (c) • Due to symmetry at the level of background these two regions predict • the same • For and • From Planck experiment, within (when ) • If as promised by CMBPOL

14. Hilltop Regions (b) and (c) & • Symmetry breaks down at the quantum level. • In region (b), the lightest mode is gauge mode • In region (c), the lightest mode is mode • Around the isocurvature modes can act as preheat fields. The couplings • of preheat fields to the inflaton are known. at the peak frequency Which can be observed at Chongqin HFGW detector or Birmingham HFGW experiment.

15. 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-Planckianones which yield large tensor/scalar ratio compatible with Planck. • M-flationwhich 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 tohierarchical 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]

16. Conclusions & Future Directions • The loop corrections from interactions of the graviton with the scalar field create the • term if . 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-flationhas a natural built-in mechanism of preheating to end inflation around the • 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

17. Thank you