| Summary: | In this paper, we introduce a new type of matter that has origin in <i>p</i>-adic strings, i.e., strings with a <i>p</i>-adic worldsheet. We investigate some properties of this <i>p</i>-adic matter, in particular its cosmological aspects. We start with crossing symmetric scattering amplitudes for <i>p</i>-adic open strings and related effective nonlocal and nonlinear Lagrangian which describes tachyon dynamics at the tree level. Then, we make a slight modification of this Lagrangian and obtain a new Lagrangian for non-tachyonic scalar field. Using this new Lagrangian in the weak field approximation as a matter in Einstein gravity with the cosmological constant, one obtains an exponentially expanding FLRW closed universe. At the end, we discuss the obtained results, i.e., computed mass of the scalar <i>p</i>-adic particle, estimated radius of related closed universe and noted <i>p</i>-adic matter as a possible candidate for dark matter.
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