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  • Chaichian, M.; Ghalee, A.; Kluson, J. (2017)
    We investigate the metric perturbations of the restricted f(R) theory of gravity in the cosmological context and explore the phenomenological implications of this model. We show that it is possible to construct a restricted model of gravity, in which the background equations are the same as the equations of motion which are derived from the Einstein-Hilbert action with the cosmological constant term. We argue that the deviation from the Einstein-Hilbert model emerges in the perturbed equations, for which we have a nonvanishing anisotropic stress. Further, with the help of the results of Planck data for the modified gravity, we obtain constraints on the parameters of the model.
  • Chaichian, M.; Ghalee, A.; Kluson, J. (2016)
    We investigate the f(R) theory of gravity with broken diffeomorphism due to the change of the coefficient in front of the total divergence term in the (3 + 1) decomposition of the scalar curvature. We perform the canonical analysis of this theory and show that its consistent form, i.e. with no unphysical degrees of freedom, is equivalent to the low-energy limit of the nonprojectable f(R) Horava-Lifshitz theory of gravity. We also analyze its cosmological solutions and show that the de Sitter solution can be obtained also in the case of this broken symmetry. The consequences of the proposed theory on the asymptotic solutions of a few specific models in the cosmological context are also presented.