Non-local SFT tachyon and cosmology

Cosmological scenarios built upon the generalized non-local String Field Theory and p-adic tachyons are examined. A general kinetic operator involving an infinite number of derivatives is studied as well as arbitrary parameter p. The late time dynamics of just the tachyon around the non-perturbative vacuum is shown to leave the cosmology trivial. A late time behavior of the tachyon and the scale factor of the FRW metric in the presence of the cosmological constant or a perfect fluid with w > -1 is constructed explicitly and a possibility of non-vanishing oscillations of the total effective state parameter around the phantom divide is proven.