Effective Field Theory of Multifield Inflation
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This document discusses the effective field theory of multi-field inflation based on Weinberg's approach. It constructs the most general Lagrangian for the background and perturbation terms up to fourth order. For the multi-field case, the Lagrangian contains terms for both the adiabatic and entropy perturbations. The validity of the effective field theory constrains the possible amplitude of non-Gaussianities produced during inflation. This approach differs from previous work by defining perturbations before distinguishing adiabatic and entropy modes.
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E05731721
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NITheP WITS node seminar: Prof Jacob Sonnenschein (Tel Aviv University) TITLE...
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1 electromagnetic induction
1. Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a circuit. This can be caused by changing the magnetic field strength, coil area, or relative orientation between the coil and magnetic field.
2. Faraday's experiments demonstrated that a changing magnetic flux induces a current in a circuit. His laws of electromagnetic induction state that an emf is induced proportional to the rate of change of magnetic flux through a circuit.
3. Lenz's law specifies that the induced current will flow in a direction to oppose the change producing it, in accordance with the law of conservation of energy.
1_electromagnetic_induction.ppt
This document summarizes key concepts related to electromagnetic induction:
1. It defines magnetic flux and describes how it can be changed by altering the magnetic field strength, coil area, or orientation to the field.
2. It outlines Faraday's experiments which demonstrated that a changing magnetic flux induces an electromotive force (emf) in a circuit.
3. It states Faraday's laws of induction and Lenz's law, describing the direction of the induced current.
4. It provides various methods for inducing an emf, including changing the magnetic field, coil area or orientation, and describes applications like generators and eddy currents.
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Effective Field Theory of Multifield Inflation
- 1. Effective Field Theory of Multi-Field Inflation a la Weinberg Nima Khosravi African Institute for Mathematical Sciences arXiv:1203.2266
- 2. map: keywords: Effective Field Theory, Inflation
- 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. EFT for Multi-Field Inflation the most general form of Lagrangian up to the 4th order derivatives: after simplifications: before simplifications!
- 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. perturbations: multi-field case: background terms: perturbations!
- 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. perturbations: adiabatic & entropy modes adiabatic mode: entropy mode: Gordon et al. arXiv:astro-ph/0009131
- 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. shape of non-Gaussianity due to previous slide: for example: equilateral NG local NG in adiabatic mode in entropy mode --- in this formalism the “Cosine” between different kinds of NG is fixed!
- 11. amplitude of NG -- validity condition of EFT i.e. constrains the amplitude of NG! -- except if the curvature of classical (background) path be large! -- or: if by a mechanism (e.g. Vainshtein) one can modify the validity condition of EFT!
- 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 is associated to adiabatic mode! -- so in Senatore & Z., the entropy modes are added into a base with already known adiabatic mode! but -- in our case we started with zeroth order term of perturbations. -- then defined the perturbations without any distinguishability between adiabatic and entropy modes!
- 13. compare with Senatore & Zaldarriaga GR + a scalar field 1 perturbation Modification Modification (EFT) (EFT) 2 3 Cheung et al. and Senatore & Z.: 0 perturbation 1 3 Weinberg and this talk: 0 2 3
- 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. compare with Senatore & Zaldarriaga shift symmetry: due to results in which causes a new symmetry for adiabatic and entropy modes:
- 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 correction term in EFT. -- different shapes of non-Gaussianity are correlated! -- in contrast to Senatore & Zaldarriaga, we suggest EFT for multi-filed inflation should be constructed as