Criticality and big brake singularities in the tachyonic evolutions of closed Friedmann universes with cold dark matter

The evolution of a closed Friedmann universe filled by a tachyon scalar field with a trigonometric potential and cold dark matter (CDM) is investigated. A subset of the evolutions consistent to $1\sigma$ confidence level with the Union 2.1 supernova data set is identified. The evolutions of the tachyon field are classified. Some of them evolve into a de Sitter attractor, while others proceed through a pseudotachyonic regime into a sudden future singularity. Critical evolutions leading to big brake singularities in the presence of CDM are found and a new type of cosmological evolution characterized by singularity avoidance in the pseudotachyon regime is presented.

Figure 1

The fit of the luminosity distance vs redshift for the parameters $k=0.44$ and ${\mathrm{\Omega }}_m=0.315$ in the parameter plane ($y_0$, $w_0={(1+s_0^2)}^{-1}$) (upper panel for ${\mathrm{\Omega }}_K=-0.0065$, lower panel for ${\mathrm{\Omega }}_K=0$). The contours refer to the $1\sigma$ and $2\sigma$ confidence levels. The color code of ${\chi }^2$ is indicated on the vertical stripes.

Figure 2

Upper panel: the numerical evolution of the dynamical equations yields seven types of trajectories (I, IIa, IIb, IIIa, IIIb, IV and V), separated by separatrices (red). Lower panel: the pseudotachyonic evolutions of the upper right corner. We chose ${\mathrm{\Omega }}_{\mathrm{\Lambda }}=0.8$.

Figure 3

The trajectories presented on the lower panel of Fig. 2 are extended to infinity, and mapped into the interval $[0,\pi /2]$ by a conformal transformation $\sigma =\arctan ({10}^{-3}\mathrm{s})$. The pseudotachyonic and quasitachyonic regimes of each of type IV, IIIa, IIIb and V evolutions (blue), and the separatrices between types IV-IIIa, IIIa-IIIb and IIIb-V (red) are shown. The soft singularities correspond to $\sigma =\pi /2$. The evolutions labeled by numbers are identical to those represented on the lower panel of Fig. 2. The critical evolutions leading to big brake singularities in the presence of dust are (4) and (6).