Hypersurface-Invariant Approach to Cosmological Perturbations

Abstract

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.

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

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• Non-linear inflationary perturbations
• Inflation and de Sitter Holography
• Quantum fluctuations of Cosmological Perturbations in Generalized Gravity
• Holography, Diffeomorphisms, and Scaling Violations in the CMB
• The Gowdy T3 Cosmologies revisited
• Characteristics of Cosmic Time
• Covariant Fluid Dynamics: a Long Wave-Length Approximation
• Coordinate-free Solutions for Cosmological Superspace
• Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly Coupled Gravitational Systems
• A New Boundary Counterterm for Asymptotically AdS Spacetimes
• Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity
• Gravitational instabilities and faster evolving density perturbations