Anisotropic Cyclic Universe in $F(X)-V(φ)$ model

Abstract: We investigate the cosmology of a class of model with noncanonical scalar field and matter in an anisotropy background. We find fixed points and their stability which constraints equation of state parameter for the matter. This is done after expressing the Einstein equations in terms of dimensionless variables. Similarly we define a set of suitable dynamical variables for studying bouncing solutions. The condition for nonsingular bounce is obtained. Here we show, numerically, that solution that of a cyclic universe exist for the certain form of kinetic term of noncanonical scalar field and the time period of cycle depends on the kinetic term of noncanonical scalar field. In certain case we find that a cyclic universe can be approximated to be a single bouncing scenario for the entire evolution of the dynamical variables. Resemblling an eternal bouncing scenario, this model may also be free from BKL instability. Also, the univerese isotropize in the expansion phase and this isotropization can be delayed to some extent by tuning the the parameter of the model.