Mimetic F(R) Gravity

In this thesis, the field equations of Mimetic F(R) Gravity Theory with a scalar field degree of freedom and internal conformal symmetry have been obtained, which is extended F(R) gravity theories but ghost-free. Beside, we have been carried out dynamical systems analysis of this theory and analyzed its accordance to Noether symmetry, on having written point-like Lagrangian for flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in the presence of ordinary matter. Basis of the mimetic field originating the late-time (and initial era) expansion of the universe also have been described in Bianchi type-I cosmology by proposing a potential function time-dependant in terms of V(ϕ=t)=α⁄t^2 . As a main purpose, we have looked into the stability of the solutions of the bouncing and ΛCDM models by utilizing the symmetries and demonstrated that the solutions are feasible in Mimetic F(R) Gravity. We also have gained the solution with future singularity in our theory.