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 ($V(ϕ) = μ^{α+ 4} ϕ^{- α}$), we show that in the quadratic dominant stage, the density parameter of a scalar field $Ω_ϕ$ decreases as $a^{-4(α-2)/(α+2)}$ for $2<α< 6$, 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 $ρ^2$-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, resulting that $α\geq 4$ is required. This constraint also restricts the value of the 5-dimensional Planck mass, e.g. $4 \times 10^{-14}m_4 \lsim m_5 \lsim 3 \times 10^{-13}m_4$ for $α=5$. For an exponential potential model $V=μ^4\exp(-λϕ/m_4)$, 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 $ρ^2$-dominant stage, rather than the $Ω_ϕ$-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 $ρ^2$-dominant stage, which provides a wider initial condition for a successful quintessence.