Cosmological Dynamics of a Dirac-Born-Infeld field

TL;DR

This paper studies the cosmological behavior of a Dirac-Born-Infeld (DBI) field, identifying stable solutions and analyzing their implications for inflation, including a notable fixed point with constant sound speed and equation of state.

Contribution

It introduces a dynamical systems approach to analyze DBI field cosmology with arbitrary power-law or exponential potentials and warp factors, revealing new fixed points and late-time attractors.

Findings

Existence of scaling solutions under specific potential and warp-factor relations.

Discovery of a new class of fixed points initially appearing singular.

Identification of a late-time attractor with constant sound speed and $w=-1$.

Abstract

We analyze the dynamics of a Dirac-Born-Infeld (DBI) field in a cosmological set-up which includes a perfect fluid. Introducing convenient dynamical variables, we show the evolution equations form an autonomous system when the potential and the brane tension of the DBI field are arbitrary power-law or exponential functions of the DBI field. In particular we find scaling solutions can exist when powers of the field in the potential and warp-factor satisfy specific relations. A new class of fixed-point solutions are obtained corresponding to points which initially appear singular in the evolution equations, but on closer inspection are actually well defined. In all cases, we perform a phase-space analysis and obtain the late-time attractor structure of the system. Of particular note when considering cosmological perturbations in DBI inflation is a fixed-point solution where the Lorentz factor is a finite large constant and the equation of state parameter of the DBI field is $w=-1$. Since in this case the speed of sound $c_s$ becomes constant, the solution can be thought to serve as a good background to perturb about.