Tachyon dark energy models: Dynamics and constraints

We explore the dynamics of dark energy models based on a Dirac-Born-Infeld (DBI) tachyonic action, studying a range of potentials. We numerically investigate the existence of tracking behavior and determine the present-day value of the equation of state parameter and its running, which are compared with observational bounds. We find that tachyon models have quite similar phenomenology to canonical quintessence models. While some potentials can be selected amongst many possibilities and fine-tuned to give viable scenarios, there is no apparent advantage in choosing a DBI scalar field instead of a Klein-Gordon one.

Figure 1

Present value of the barotropic index $w$ for tachyon tracking solutions (squares) and for creeping solutions for $T_{\mathrm{i}}=1$ (circles) with inverse power-law potentials $U\propto T^{-\beta }$. For comparison the result for tracking canonical quintessence is also shown (triangles).

Figure 2

Evolution of the density parameters and equation of state as a function of $N$ for the inverse power-law tachyon model with $\beta =1/3$. Solid line: ${\varrho }_{\mathrm{m}}/x$; dashed line: ${\varrho }_{\mathrm{r}}/x$; dotted line: ${\varrho }_T/x$. The dot-dashed line is the barotropic index $w$.

Figure 3

Numerical points in the $w_0\mathrm{\text{−}}{w}_0^{\prime }$ plane for tracking solutions (squares) and creeping solutions for $T_{\mathrm{i}}=1$ (circles) with inverse power-law potentials $U\propto T^{-\beta }$. The value of $\beta$ is shown at each point, while the dotted lines are the $1\sigma$ and $2\sigma$ likelihood bounds [13]. The unlabeled points on the left and right of $\beta =1$ in the tracking curve are $\beta =0.95$ and $\beta =1.05$, respectively.

Figure 4

Evolution as a function of $N$ of the model $U=U_c/\cosh (T)$, in this case extending beyond the present. Solid line: ${\varrho }_{\mathrm{m}}/x$; dashed line: ${\varrho }_{\mathrm{r}}/x$; dotted line: ${\varrho }_T/x$. The dot-dashed and dot-dot-dashed lines are $w$ and $w^{\prime }$, respectively. In this example, the initial condition is $T_{\mathrm{i}}=0.5$, for which $w_0\approx -0.98$ and $w_0^{\prime }\approx 0.03$.