SÉMINAIRE DU GRECO
"Exploring the cosmological observations for signatures of extra dimensions" |
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Y. Takamizu |
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We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a single scalar field with a general kinetic term and a general form of the potential. We employ the ADM formalism and the spatial gradient expansion approach, characterised by O(?m), where ?=1/(HL) as a small parameter representing a ratio of the Hubble length to the characteristic length scale L of perturbations. By this formalism, we obtain general solutions of full nonlinear curvature perturbations valid up to the second-order in the expansion ( m=2 ). We can derive a simple second-order differential equation for a nonlinear variable as an extension of linear curvature perturbation in the comoving hypersurface valid up to this order, which includes full-order perturbations in the standard perturbation theory. We consider a general formalism that the nonlinear solutions in the next-leading order ( m=2 ) in the gradient expansion are matched to the solutions of the n-th-order perturbation after horizon crossing. This formulation can be applied to calculating a superhorizon evolution of primordial non-Gaussianity beyond the so-called ?N formalism or Separate universe approach (that is the leading order m=0 ). The approach beyond ?N formalism can investigate a temporal violation of slow-roll conditions, and our formalism can be applied to the cases for both a canonical and a non-canonical scalar field (e.g. DBI inflation). As a leading order connection in our formalism, we investigate the nonlinear solution matched to a linear solution ( n=1 ) after horizon exit. For a simple example, we consider a single-field inflation of Starobinsky''s model, having a stage at which slow-roll conditions are broken temporarily. We find that a large non-Gaussianity can be enhanced by a sudden change of the potential''s slope in just a single-field superhorizon dynamics. |
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mercredi 17 mars 2010 - 11:00 Salle des séminaires Évry Schatzman, Institut d'Astrophysique de Paris |
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