Hypersurface-Invariant Approach to Cosmological Perturbations

Details Hypersurface-Invariant Approach to Cosmological Perturbations Hypersurface-Invariant Approach to Cosmological Perturbations

1994-09-22

arxiv.org/abs/astro-ph/9409055v1

Phys.Rev.D51:517-535,1995

Astronomy and Astrophysics

Astrophysics

51 pages, Latex 2.09 ALBERTA THY/20-94, DAMTP R94/25 To appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.51.517

Using Hamilton-Jacobi theory, we develop a formalism for solving semi-classical cosmological perturbations which does not require an explicit choice of time-hypersurface. The Hamilton-Jacobi equation for gravity interacting with matter (either a scalar or dust field) is solved by making an Ansatz which includes all terms quadratic in the spatial curvature. Gravitational radiation and scalar perturbations are treated on an equal footing. Our technique encompasses linear perturbation theory and it also describes some mild nonlinear effects. As a concrete example of the method, we compute the galaxy-galaxy correlation function as well as large-angle microwave background fluctuations for power-law inflation, and we compare with recent observations.

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