Abstract
The relevance of quantum rolling tachyons and corresponding inflation scenario in the frame of the standard, p-adic and adelic cosmology are reviewed. The field theory of tachyon matter proposed by Sen in a zero-dimensional version leads to a number of models with a particle moving under different potentials. We consider quantum propagators of the models, as well as, the vacuum states and conditions necessary to construct an adelic generalization. In addition we present inflationary scenarios for some interesting models based on analytic and numeric calculations. A brief overview of the state of art in the field and suggestions for further consideration close the paper.
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