# Cosmological stability of Weyl conformal tensor

* E. Goulart and M. Novello*^{1}

(1) Institute of Cosmology, Relativity and Astrophysics ICRA/CBPF, Rua Dr. Xavier Sigaud 150, Urca 22290-180 Rio de Janeiro, RJ-Brazil

### Abstract

We show that the conformal structure of the Friedmann-Robertson-Walker geometry is asymptotically stable with respect to time under arbitrary scalar perturbations. The analysis was undertaken for the Euclidean section, using the gauge-independent quasi-Maxwellian equations of motion for the perturbations. A well-known divergence theorem of non-autonomous planar dynamical systems is used to corroborate our conclusions. In other words, from a global point of view, once the geometry arrives at a FRW stage, it is not likely to leave it, even if during a certain limited interval of time it may present inhomogeneous properties.

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