Scale-invariant Perturbation of the Friedmann Universe

Details Scale-invariant Perturbation of the Friedmann Universe Scale-invariant Perturbation of the Friedmann Universe

1997-06-17

arxiv.org/abs/astro-ph/9706181v3

Astronomy and Astrophysics

Astrophysics

extended version with new diagrams and discussions

Scientific paper

We use de Vaucouleurs' power-law density-distance relation, to study a hierarchical perturbation of the Friedmann universe. We solve the Einstein equation and obtain the density contrast and the amplification factor for the perturbation. It is shown that, scale-invariant inhomogeneities decay in Einstein-de-Sitter universe. On the contrary, in an open universe, the inhomogeneities grow. For low values of $\Omega$, amplification peaks sharply and the fluctuations can grow by up to a factor of $10^{13}$ from the recombination to the present time. Our analysis of the closed universe further confirms that, unlike the common belief that perturbations grow faster with increasing $\Omega$, scale-invariant perturbations amplify with decreasing $\Omega$. This result is consistent with the very low density expected for a hierarchical universe.

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