Year: 2001
Type: article
Abstract: We reanalyze a new quintessence scenario in a brane world model, assuming that a quintessence scalar field is confined in our three-dimensional brane world. We study three typical quintessence models: (1) an inverse-power-law potential, (2) an exponential potential, and (3) a kinetic-term quintessence $(k$-essence) model. With an inverse-power-law potential model $[V(\ensuremath{\varphi})={\ensuremath{\mu}}^{\ensuremath{\alpha}+4}{\ensuremath{\varphi}}^{\ensuremath{-}\ensuremath{\alpha}}],$ we show that in the quadratic dominant stage the density parameter of a scalar field ${\ensuremath{\Omega}}_{\ensuremath{\varphi}}$ decreases as ${a}^{\ensuremath{-}4(\ensuremath{\alpha}\ensuremath{-}2)/(\ensuremath{\alpha}+2)}$ for $2<\ensuremath{\alpha}<6,$ which is followed by the conventional quintessence scenario. This feature provides us wider initial conditions for successful quintessence. In fact, even if the universe is initially scalar-field dominated, it eventually evolves into a radiation dominated era in the ${\ensuremath{\rho}}^{2}$-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, with the result that $\ensuremath{\alpha}>~4$ is required. This constraint also restricts the value of the five-dimensional Planck mass, e.g., $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{m}_{4}\ensuremath{\lesssim}{m}_{5}\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{m}_{4}$ for $\ensuremath{\alpha}=5.$ For an exponential potential model $V={\ensuremath{\mu}}^{4}\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}\ensuremath{\varphi}{/m}_{4}),$ 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 the ${\ensuremath{\rho}}^{2}$-dominant stage, rather than the ${\ensuremath{\Omega}}_{\ensuremath{\varphi}}$-decreasing solution for an inverse-power-law potential. Then we do find a slight advantage in a brane world. Only the density parameter increases more slowly in the ${\ensuremath{\rho}}^{2}$-dominant stage, which provides a wider initial condition for successful quintessence.
Authors: Shuntaro Mizuno, Kei-ichi Maeda
Institution: Waseda University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2096777527