Cosmology with decaying tachyon matter

We investigate the case of a homogeneous tachyon field coupled to gravity in a spatially flat Friedmann-Robertson-Walker spacetime. Assuming the field evolution to be exponentially decaying with time we solve the field equations and show that, under certain conditions, the scale factor represents an accelerating universe, following a phase of decelerated expansion. We make use of a model of dark energy (with $p=-\rho$) and dark matter ($p=0$) where a single scalar field (tachyon) governs the dynamics of both the dark components. We show that this model fits the current supernova data as well as the canonical $\Lambda \mathrm{CDM}$ model. We give the bounds on the parameters allowed by the current data.

Figure 1

We plot the potential $V(T)$ as a function of the field $T$ in arbitrary units. The values of the model parameters for this and the next figure are taken from best fit to the current supernova data given later.

Figure 2

Potential as a function of time. The field rolls down from top of the potential and after infinite time interval reaches a constant value.

Figure 3

This plot shows how ${\Omega }_{DM}$ (solid curve) and ${\Omega }_{DE}$ (dashed curve) evolve with redshift in our best-fit model. The universe is completely dominated by matter beyond a redshift $z\sim 10$.

Figure 4

The innermost, middle, and the outermost contours correspond to $68\%$, $90\%$, and $95\%$ confidence level, respectively. Peak of likelihood surface corresponds to $p/r=0.385$, $s=0.66$. The asterisk marks the minimum of ${\chi }^2$. As discussed in the text, to keep the potential physical at all times we must impose the constraint $s\ge 2/3$. We find that the maximum of the probability density lies at the edge of this interval.

Figure 5

The solid curve is the Hubble plot for the best-fit model with $p/r=0.385$, $s=0.66$, and $H_0=64.0$. For comparison we also show the best-fit $\Lambda CDM$ model (dashed curve).

Figure 6

The deceleration parameter calculated for the best-fit model as in previous figure. We see that the universe starts decelerating around $z\sim 1$.