Astronomy and Astrophysics – Astrophysics
Scientific paper
2006-10-03
JCAP 0702:017,2007
Astronomy and Astrophysics
Astrophysics
45 pages. v3: corrected Eqs. (213), (220), (221) and (225)
Scientific paper
10.1088/1475-7516/2007/02/017
We present a covariant formalism for studying nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential equations governing the evolution of these two covectors, as well as the evolution equation for the covector associated with the curvature perturbation. The form of these equations is very close to the analogous equations obtained in the linear theory, but our equations are fully nonlinear and exact. As an application of our formalism, we expand these equations at second order in the perturbations. On large scales, we obtain a closed system of coupled scalar equations giving the evolution of the second-order adiabatic and entropy perturbations in terms of the first-order perturbations. These equations in general contain a nonlocal term which, however, rapidly decays in an expanding universe.
Langlois David
Vernizzi Filippo
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