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

## TL;DR

This paper explores a tachyon cosmological model within a braneworld scenario, revealing how a power-law warp factor influences the universe's evolution, leading to dust-like or quasi de Sitter behaviors depending on the potential's power.

## Contribution

It introduces a generalized braneworld model with an inverse power-law tachyon potential, analyzing the resulting cosmological dynamics and identifying a critical power dividing different universe behaviors.

## Key findings

- Identifies a critical power n_cr separating dust and quasi de Sitter universes.
- Shows the impact of warp factor on the effective gravitational constant.
- Derives asymptotic behaviors based on the potential's power.

## 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 $V\propto \varphi^{-n}$ of the tachyon field $\varphi$. We find a critical power $n_{\rm cr}$ that divides two subclasses with distinct asymptotic behaviors: a dust universe for $n>n_{\rm cr}$ and a quasi de Sitter universe for $0<n<n_{\rm cr}$.