Interacting tachyon: Cosmological evolution for a tachyon and a scalar field

Abstract

We study the cosmological evolution of a tachyon scalar field $T$ with a Dirac-Born-Infeld type Lagrangian and potential $V(T)$ coupled to a canonically normalized scalar field $\ensuremath{\phi}$ with an interaction term $B(T,\ensuremath{\phi})$ in the presence of a barotropic fluid ${\ensuremath{\rho}}_{b}$, which can be matter or radiation. The force between the barotropic fluid and the scalar fields is only gravitational. We show that the dynamics is completely determined by only three parameters ${\ensuremath{\lambda}}_{1}=\ensuremath{-}{V}_{T}/{V}^{3/2}$, ${\ensuremath{\lambda}}_{2}=\ensuremath{-}{B}_{T}/{B}^{3/2}$, and ${\ensuremath{\lambda}}_{3}=\ensuremath{-}{B}_{\ensuremath{\phi}}/B$. We determine analytically the conditions for ${\ensuremath{\lambda}}_{i}$ under which the energy density of $T$, $\ensuremath{\phi}$, and ${\ensuremath{\rho}}_{b}$ have the same redshift. We study the behavior of $T$ and $\ensuremath{\phi}$ in the asymptotic limits for $\ensuremath{\lambda}$ and we show the numerical solution for different interesting cases. The effective equation of state for the tachyon field changes due to the interaction with the scalar field and we show that it is possible for a tachyon field to redshift as matter in the absence of an interaction term $B$ and as radiation when $B$ is turned on. This result solves then the tachyonic matter problem.