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# Effective Field Theory of Multifield Inflation

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### Effective Field Theory of Multifield Inflation

1. 1. Effective Field Theory ofMulti-Field Inflation a la Weinberg Nima KhosraviAfrican Institute for Mathematical Sciences arXiv:1203.2266
2. 2. map: keywords: Effective Field Theory, Inflation
3. 3. Effective Field Theory an effective theory: is true for a certain domain of energy. two cases:  as a part of a true theory for whole energy scales  using EFT to simplify calculations!  in lack of a complete theory for the energy scales of interests  using EFT since there is no other choice!  constructing EFT, by considering e.g. symmetry properties of the model. 
4. 4. EFT for Multi-Field Inflation the most general form of Lagrangian up to the 4th order derivatives: after simplifications: before simplifications!
5. 5. perturbations: perturbations in single field model (Weinberg’s paper) -- it is up to 4th order of perturbations automatically. -- speed of sound ≠ 1 -- large non-Gaussianity ? -- speed of sound is constrained by validity of EFT!
6. 6. perturbations: multi-field case: background terms: perturbations!
7. 7. perturbations: two-field case: the most general form of the Lagrangian: second order perturbations!…. and cubic and quartic terms!. . . transition to adiabatic and entropy curvature perturbations! 
8. 8. perturbations: adiabatic & entropy modes adiabatic mode: entropy mode: Gordon et al. arXiv:astro-ph/0009131
9. 9. perturbations: adiabatic & entropy modes  as an example: second order perturbation terms (containing time derivatives) due to correction term: note that just these two combinations appear in this formalism!
10. 10. shape of non-Gaussianity due to previous slide: for example: equilateral NG local NGin adiabatic mode in entropy mode--- in this formalism the “Cosine” between different kinds of NG is fixed!
11. 11. amplitude of NG-- validity condition of EFT i.e. constrains theamplitude of NG!-- except if the curvature of classical (background) path be large!-- or: if by a mechanism (e.g. Vainshtein) one can modify the validitycondition of EFT!
12. 12. compare with Senatore & Zaldarriaga-- Senatore & Zaldarriaga model is based on Cheung et al.’s work!-- in Cheung’s work, EFT is constructed on perturbations’ level! -- since their model is single field, the perturbation isassociated to adiabatic mode!-- so in Senatore & Z., the entropy modes are added into a base withalready known adiabatic mode!but-- in our case we started with zeroth order term of perturbations. -- then defined the perturbations without any distinguishabilitybetween adiabatic and entropy modes!
13. 13. compare with Senatore & Zaldarriaga GR + a scalar field 1 perturbation Modification Modification (EFT) (EFT) 2 3Cheung et al. and Senatore & Z.: 0 perturbation 1 3Weinberg and this talk: 0 2 3
14. 14. compare with Senatore & Zaldarriaga so in Senatore & Zaldarriaga, the shift symmetry results in a Lagrangian similar toi.e. there are just derivatives of adiabatic and entropy perturbations! but in our model the case is different!
15. 15. compare with Senatore & Zaldarriaga shift symmetry: due toresults inwhich causes a new symmetry for adiabatic and entropy modes:
16. 16. conclusions-- this model does not predict a large non-Gaussianity except: -- for a highly curved classical path in phase-space! -- or if a shielding mechanism allows large first correctionterm in EFT.-- different shapes of non-Gaussianity are correlated!-- in contrast to Senatore & Zaldarriaga, we suggest EFT formulti-filed inflation should be constructed as
17. 17. thank you!