Towards p-Adic Matter in the Universe
  Starting from p-adic string theory with tachyons, we introduce a new kind of
non-tachyonic matter which may play an important role in evolution of the
Universe. This matter retains nonlocal and nonlinear p-adic string dynamics,
but does not suffer of negative square mass. In space-time dimensions D = 2 +
4k, what includes D = 6, 10, ..., 26, the kinetic energy term also maintains
correct sign. In these spaces this p-adic matter provides negative cosmological
constant and time-dependent scalar field solution with negative potential.
Their possible cosmological role is discussed. We have also connected
non-locality with string world-sheet in effective Lagrangian for p-adic string.
