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Black hole information problem is the question about unitarity of theevolution operator during the collapse and evaporation of the black hole. Onecan ask the same question about unitarity of quantum and inflationarycosmology. In this paper we argue that in both cases, for black holes and forcosmology, the answer is negative and we face non-unitarity.  Such a question can not be addressed by using the fixed classicalgravitational background since one has to take into account the backreaction.To his end one uses the semi-classical gravity, which includes the expectationvalue of the energy - momentum tensor operator of the matter fields. One has torenormalize the energy-momentum tensor and one gets an effective action whichcontains quadratic terms in scalar curvature and Ricci tensor. Such quadraticgravity contains ghosts which in fact lead to violation of unitarity in blackholes and cosmology. We discuss the question whether black holes will emitghosts.  One can try to restrict ourselves to the $f(R)$ gravity that seems is a goodapproximation to the semi-classical gravity and widely used in cosmology. Theblack hole entropy in $f(R)$ gravity is different from the Bekenstein-Hawkingentropy and from entanglement island entropy. The black hole entropy in $R+R^2$gravity goes to a constant during the evaporation process. This can beinterpreted as another indication to the possible non-unitarity in black holesand cosmology

Information Problem in Black Holes and Cosmology and Ghosts in Quadratic Gravity