Gradient expansion approach to nonlinear superhorizon perturbations

Details Gradient expansion approach to nonlinear superhorizon perturbations Gradient expansion approach to nonlinear superhorizon perturbations

2006-12-29

arxiv.org/abs/gr-qc/0612191v3

Prog.Theor.Phys.117:633-654,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, no figures. V2: minor changes, typos corrected; V3:Section I, Introduction and minor change to match version to appe

Scientific paper

10.1143/PTP.117.633

Using the gradient expansion approach, we formulate a nonlinear cosmological perturbation theory on super-horizon scales valid to $O(\epsilon^2)$, where $\epsilon$ is the expansion parameter associated with a spatial derivative. For simplicity, we focus on the case of a single perfect fluid, but we take into account not only scalar but also vector and tensor modes. We derive the general solution under the uniform-Hubble time-slicing. In doing so, we identify the scalar, vector and tensor degrees of freedom contained in the solution. We then consider the coordinate transformation to the synchronous gauge in order to compare our result with the previous result given in the literature. In particular, we find that the tensor mode is invariant to $O(\epsilon^2)$ under the coordinate transformation.

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