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The Einstein-Vlasov-Scalar Field System with Gowdy or $T^2$ Symmetry in Contracting Direction
Alex Lassiye Tchuani
,
David Tegankong
,
Norbert Noutchegueme
Abstract
We prove in the case of cosmological models for the Einstein-Vlasov-scalar field system with Gowdy symmetry, that the solutions exist globally in the past. The sources of the equations are generated by a distribution function and a scalar field, subject to the Vlasov and the wave equations respectively. The result is generalized for the case of $T^2$ symmetry. Using previous results, we deduce geodesic completeness.