We study the stability of f (R)-AdS (Schwarzschild-AdS) black hole obtained from f (R) gravity. In order to resolve the difficulty of solving fourth order linearized equations , we transform f (R) gravity into the scalar-tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar becomes a dynamical scalaron, showing that all linearized equations are second order. Using the positivity of gravitational potentials and S-deformed technique allows us to guarantee the stability of f (R)-AdS black hole if the scalaron mass squared satisfies the Breitenlohner-Freedman bound. This is confirmed by computing quasinormal frequencies of the scalaron for f (R)-AdS black hole.

We investigate a nonsingular initial state of the Universe which leads to inflation naturally. The model is described by a scalar field with a quadratic potential in Eddington-inspired Born-Infeld gravity. The curvature of this initial state is given by the mass scale of the scalar field, which is much smaller than the Planck scale. Therefore, in this model, quantum gravity is not necessary in understanding this preinflationary stage, no matter how large the energy density becomes. The initial state in this model evolves eventually to a long inflationary period which is similar to the usual chaotic inflation.

We investigate the evolution of the Universe filled with barotropic perfect fluid in Eddingtoninspired Born-Infeld gravity. We consider both the isotropic and the anisotropic universe.At the early stage when the energy density is high, the evolution is modified considerably compared with that in general relativity. For the equation-of-state parameter w > 0, the initial singularity is not accompanied as it was discovered for radiation in earlier work. More interestingly, for pressureless dust (w = 0), the initial state approaches a de Sitter state.This fact opens a new possibility of singularity-free nature of the theory. The anisotropy is mild, and does not develop curvature singularities in spacetime contrary to general relativity. Conclusions 16A Energy-Momentum Conservation 17 B Scale Factor a(t) for p = 0 19

We study the stability of the BTZ black hole in the new massive gravity. This is a nontrivial task because the linearized equation around the BTZ black hole background is a fourth-order differential equation. Away from the critical point of m 2 ' 2 ¼ 1=2, this fourth-order equation is split into two secondorder equations: one describes a massless graviton, and the other is designed for a massive graviton, which could be obtained from the Fierz-Pauli action. In this case, calculating quasinormal modes leads to confirming the stability of the BTZ black hole. At the critical point, we derive two left-and rightlogarithmic quasinormal modes from the logarithmic conformal field theory. Finally, we identify two s massive modes propagating on the black hole background through the conventional black hole stability analysis.

We investigate the stability of an fðRÞ (Schwarzschild) black hole obtained from the fðRÞ gravity. It is difficult to carry out the perturbation analysis around the black hole because the linearized Einstein equation is fourth order in fðRÞ gravity. In order to resolve this difficulty, we transform fðRÞ gravity into the scalar-tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar becomes a scalaron, showing that all linearized equations are second order, which are the same equations for the massive Brans-Dicke theory. It turns out that the fðRÞ black hole is stable against the external perturbations if the scalaron does not have a tachyonic mass.