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Title:
Gauge-Invariant cosmological perturbationsAbstract:
The physical interpretation of perturbations of homogeneous,
isotropic cosmological models in the early Universe,when the
perturbation is larger than the particle horizon, is clarified by
defining a complete set of gauge-invariantvariables. The linearized
perturbation equations written in these variables are simpler than the
usual versions, andeasily accommodate an arbitrary background equation
of state, entropy perturbations, and anisotropic
pressureperturbations. Particular attention is paid to how a scalar
(density) perturbation might be generated by stressperturbations at
very early times, when the non-gauge-invariant perturbation in the
density itself is ill-defined. Theamplitude of the fractional energy
density perturbation at the particle horizon cannot be larger, in
order ofmagnitude, than the maximum ratio of the stress perturbation
to the background energy density at any earlier time,unless the
perturbation is inherent in the initial singularity.
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