Abstract
We construct a generic thin-shell wormhole (TSW) in the Robertson -Walker (RW) cosmological model of the Universe. The general formalism is presented and here in this paper—the first part of the research- we investigate the stability of the TSW constructed in the static RW universe. To do so, we perform two different stability analyses namely a mechanical linear radial perturbation and a small speed exact (not linearized) perturbation. It is shown that the corresponding TSW is stable against a linear radial perturbation provided that the variable equation of state of the surface energy-momentum tensor is finely tuned. On the other hand, the exact stability analysis in the context of small-speed perturbation reveals that the throat of the TSW for the closed static universe oscillates between the center of the Universe and the outer boundary.
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