Tachyon cosmology, supernovae data, and the big brake singularity

We compare the existing observational data on type Ia supernovae with the evolutions of the Universe predicted by a one-parameter family of tachyon models which we have introduced recently [Phys. Rev. D 69, 123512 (2004)]. Among the set of the trajectories of the model which are compatible with the data there is a consistent subset for which the Universe ends up in a new type of soft cosmological singularity dubbed big brake. This opens up yet another scenario for the future history of the Universe besides the one predicted by the standard $\Lambda \mathrm{CDM}$ model.

Figure 1

Phase portrait evolution for $k>0$ ($k=0.44$).

Figure 2

The fit of the luminosity distance vs redshift for $k=-0.4$ (upper left), $-0.2$ (upper right), 0 (middle left), 0.2 (middle right), 0.4 (lower left), and 0.6 (lower right), in the parameter plane [$y_0,w_0=1/(1+s_0^2)$]. The white areas represent regions where the bounds on the model are not satisfied. The contours refer to the 68.3% ($1\sigma$) and 95.4% ($2\sigma$) confidence levels. For increasing values of $|k|<1$ the well-fitting regions are increasingly smaller. The color code for ${\chi }^2$ is indicated on the vertical stripes.

Figure 3

The future evolution of those universes which are in a 68.3% confidence level fit with the supernova data. The $1\sigma$ contours (black lines in the $z=0$ plane) are from Fig. 2 [the parameter plane $(y_0,w_0)$ is the $z=0$ plane here]. The sequence of figures and the values of $k$ are the same as in Fig. 2. The short and thick (blue) line in the plane of initial conditions separates the $1\sigma$ parameter ranges for which the universe evolves into a de Sitter regime or towards the big brake singularity. Future evolutions towards the big brake singularity of the universes selected by the comparison with supernovae data become more frequent with increasing $k$.