The dynamical behavior of some modified gravitational theories has been studied to check their consistency with the current observational evidence about the different cosmological epochs. In addition we have studied the existence of Anyon Van der Waals black holes. Anyons are particles with intermediate statistics in 2+1 dimensional space-time. Our results show that only Anyon Van der Waals black holes with quasi-bosonic statistics can exist because although the Anyon Van der Waals black holes with quasi-fermionic statistics are Einstein equations solution, they don’t have physical horizon. $f(R,T,R_{\\mu \u}T^{\\mu \u})$ gravitational theory is a modified version of $f(T)$ theory which allows a more complete coupling between the geometry and matter part of the theory. Studying the dynamical behavior of this theory by using the autonomous dynamical system analysis shows that the cosmological epochs and their stability in this theory, is consistent with our expectation. Furthermore the late time behavior of this gravitational theory will make an extension to the members of a class of future singularities of the universe by adding a new member to it. The stability of the fixed points of Horava-Lifshitz gravitational theory with both dark energy and cosmological constant to be the energy components of the universe, we have shown that the dark energy epoch is a saddle fixed point while the cosmological constant epoch is a stable one. This means that the universe in which the cosmological constant is dominant is the last destination of the universe we have studied here. In addition we have considered this gravitational theory by assuming more complicated equation of state for dark energy and the results show that only for certain intervals of the parameters, the theory can describe the cosmological epochs stability properly. One of the other gravitational theory is a universe which a boundary screen has been considered for it. As a result, there will be two additional terms in the equations of motion which will make changes in the dynamical behavior of the universe. The dynamical consideration of this theory puts boundaries on the values of $C_1$ and $C_2$ to make the cosmological epochs ordering consistent with the observation. We have also investigated the theory in the absence of dark energy and the results show that instead of dark energy, the entropic force terms can describe the present accelerated expansion of the universe. It is also interesting to see that considering both dark energy and entropic force to be the energy components of the universe will lead us to this output that depending on the equation of state of dark energy, the dark energy epoch will be a saddle point while the entropic force universe represents a stable fixed point. In addition to these, we have presented some features of primordial gravitational waves. Their equations of motion and constraints have been presented for different epochs for in the Einstein-Hilbert background gravity. In this way the effect of relativistic degrees of freedom and second horizon crossing on them, have been applied to the equations. Primordial gravitational waves are great messengers of the very beginning of the universe and their detectability is quite important. The solution of their equation of motion will give us a set of information to check if they can be detectable in the near future. The point is that their energy density and detectability depends on the background gravity. Thus the results of the other sections will be used in our future studies to determine the gravitational waves energy density and detectability in different modified gravitational theories.