Quintessence in a Brane World

Abstract

We reanalyze a new quintessence scenario in a brane world model, assuming that a quintessence scalar field is confined in our 3-dimensional brane world. We study three typical quintessence models : (1) an inverse-power-law potential, (2) an exponential potential, and (3) kinetic-term quintessence ($k$-essence) model. With an inverse power law potential model ($V(\varphi )={\mu }^{\alpha +4}{\varphi }^{-\alpha }$), we show that in the quadratic dominant stage, the density parameter of a scalar field ${\Omega }_{\varphi }$ decreases as $a^{-4(\alpha -2)/(\alpha +2)}$ for $2<\alpha <6$, which is followed by the conventional quintessence scenario. This feature provides us wider initial conditions for a successful quintessence. In fact, even if the universe is initially in a scalar-field dominant, it eventually evolves into a radiation dominant era in the ${\rho }^2$-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, resulting that $\alpha \ge 4$ is required. This constraint also restricts the value of the 5-dimensional Planck mass, e.g. $4\times 10^{-14}{m}_4\text{lsim}{m}_5\text{lsim}3\times 10^{-13}{m}_4$ for $\alpha =5$. For an exponential potential model $V={\mu }^4\exp (-\lambda \varphi /m_4)$, we may not find a natural and successful quintessence scenario as it is. While, for a kinetic-term quintessence, we find a tracking solution even in ${\rho }^2$-dominant stage, rather than the ${\Omega }_{\varphi }$-decreasing solution for an inverse-power-law potential. Then we do find a little advantage in a brane world. Only the density parameter increases more slowly in the ${\rho }^2$-dominant stage, which provides a wider initial condition for a successful quintessence.

Comments: 17 pages, 9 figures, submitted to Physical Review D