Dynamical System Approach and Thermodynamical Perspective of Hořava-Lifshitz Gravity

The authors have examined a Friedmann Robertson Walker cosmological model in Hořava-Lifshitz gravity by using a dynamical system approach. A set of autonomous equations is derived and their solutions are calculated. The critical points from these equations and find the characteristics values with the analysis of the physical interpretation of the phase space for this system are assessed. Three stable critical points are found and the values of the physical parameters and the scale factor's expressions at each critical points are displayed in Tables 1, 2, and 3. A hybrid scale factor to develop the model, which results in a phase transition from deceleration to acceleration is used. The suitable values of the parameters are governed by applying the Monte Chain Monte Carlo method technique to the Hubble 46 and joint Hubble 46 and Baryon Acoustic Oscillations 15 datasets. In contrast to the negative behavior of pressure, the positive behavior of energy density and $q=-1$ illustrate the Universe's acceleration epoch and the $\Lambda \mathrm{CDM}$ model is represented by the EoS parameter $\omega =-1$. The authors investigated that the energy conditions and their model violates the strong energy condition. Utilizing $Om$ diagnostic test, it is found that the model represents phantom behavior. The thermodynamical perspective for the model is also examined. The model accurately explained the Universe's propagation history and fits well with contemporary cosmic data.