Beyond δn formalism

Atsushi Naruko, Yu Ichi Takamizu, Misao Sasaki

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a multicomponent scalar field with a general kinetic term and a general form of the potential in the context of inflationary cosmology. We employ the ADM formalism and the spatial gradient expansion approach, characterized by O(ε2), where ε = 1/(HL) is a small parameter representing the ratio of the Hubble radius to the characteristic length scale L of perturbations. We provide a formalism to obtain the solution in the multi-field case. This formalism can be applied to the superhorizon evolution of a primordial non-Gaussianity beyond the so-called δN formalism which is equivalent to O(ε 0) of the gradient expansion. In doing so, we also derive fully nonlinear gauge transformation rules valid through O(ε 2). These fully nonlinear gauge transformation rules can be used to derive the solution in a desired gauge from the one in a gauge where computations are much simpler. As a demonstration, we consider an analytically solvable model and construct the solution explicitly.

Original languageEnglish
Article number043E01
JournalProgress of Theoretical and Experimental Physics
Issue number4
Publication statusPublished - 2013 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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