Cosmology of rolling tachyon

Recent analysis of string theory 1,2,3 suggests that classical dynamics of tachyon on an unstable D-brane is described by a scalar Born-Infeld type action with a runaway potential 4. Characteristic of such tachyon effective theory is absence of perturbative tachyonic modes around the potential minimum and existence of spatially homogeneous rolling tachyon configuration 5. In the background of the rolling tachyon, Abelian gauge field on the D-brane cannot support perturbative spectrum at late-time 6,7,9. In this review, we summarize firstly bosonic effective action both in the bulk and on the D-brane, together with shapes of the tachyon potential. In section 3, we introduce Carrolian limit, and then discuss nonexistence of perturbative spectra of the tachyon and the Abelian gauge field in the potential minimum, of which dynamics are governed by nonlocal D-brane action. For the tachyon, there exists the classical rolling tachyon solution connecting smoothly unstable maximum