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Conserved Quantities in Perturbed Inflationary Universes

Peter Dunsby·Marco Bruni
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Abstract

Given that observations seem to favour a \index{density parameter} $Ω_0<1$, corresponding to an open universe, we consider gauge\hs invariant perturbations of non\hs flat Robertson\hs Walker universes filled with a general imperfect fluid which can also be taken to represent a scalar field. Our aim is to set up the equations that govern the evolution of the density perturbations $Δ$ so that it can be determined through a {\it first order differential equation} with a quantity $\kk$ which is conserved at any length scale, even in non\hs flat universe models, acting as a source term. The quantity $\kk$ generalizes other variables that are conserved in specific cases (for example at large scales in a flat universe) and is useful to connect different epochs in the evolution of density perturbations via a transfer function. We show that the problem of finding a conserved $\kk$ can be reduced to determining two auxiliary variables $X$ and $Y$, and illustrate the method with two simple examples.

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Peter Dunsby, Marco Bruni. 1994-05-04. Conserved Quantities in Perturbed Inflationary Universes. https://doi.org/10.1142/s0218271894000629

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