Tachyon with an inverse power-law potential in a braneworld cosmology

Abstract

We study a tachyon cosmological model based on the dynamics of a 3-brane in the bulk of the second Randall-Sundrum model extended to more general warp functions. A well known prototype of such a generalization is the bulk with a selfinteracting scalar field. As a consequence of a generalized bulk geometry the cosmology on the observer brane is modified by the scale dependent four-dimensional gravitational constant. In particular we study a power law warp factor which generates an inverse power-law potential V ∝ ϕ −n of the tachyon field ϕ. We find a critical power n cr that divides two subclasses with distinct asymptotic behaviors: a dust universe for n > n cr and a quasi de Sitter universe for 0 < n < n cr .

Particle creation and reheating in a braneworld inflationary scenario

“…It has been shown [8,22] that the energy density of the tachyon with an inverse power potential yields asymptotically either dust or quasi de sitter universe, with the cosmological scale dependence as ρ tach ∝ a −3 or 1/ log a, respectively. Since the radiation density behaves as ρ rad ∝ a −4 , sooner or later ρ tach will inevitably dominate the radiation.…”

“…where the functional form of χ(z) depends on the selfinteraction potential of the bulk scalar field [22]. For a pure AdS bulk χ = z/ℓ with ℓ being the AdS curvature radius.…”

“…In the spatially flat BWC the Hubble expansion rate H is related to the Hamiltonian via a modified Friedmann equation [22] which can be written as…”

“…It is worth noting that the cosmological particle creation vanishes exactly for n = 1/2. This power precisely equals the critical power at which the tachyon cosmology changes from dust to quasi-de Sitter [8,22]. To estimate the tachyon energy density we can use the expression (69) with σ estimated by the inequality (73) in which χ ,θ is set to 1 yielding…”

“…Note that the cosmological particle creation vanishes exactly for n = 1/3. Again, this power precisely equals the critical power at which the tachyon cosmology changes from dust to quasi-de Sitter [22].…”