Hybrid metric-Palatini brane system

It is known that the metric and Palatini formalisms of gravity theories have their own interesting features but also suffer from some different drawbacks. Recently, a novel gravity theory called hybrid metric-Palatini gravity was put forward to cure or improve their individual deficiencies. The action of this gravity theory is a hybrid combination of the usual Einstein-Hilbert action and a f (R ) term constructed by the Palatini formalism. Interestingly, it seems that the existence of a light and long-range scalar field in this gravity may modify the cosmological and galactic dynamics without conflicting with the laboratory and Solar System tests. In this paper, we focus on the tensor and scalar perturbations of the thick branes in this novel gravity theory. We consider two models as examples, namely, the thick branes constructed by a background scalar field and by pure gravity. The thick branes in both models have no inner structure. However, affected by the hybrid combination of the metric and Palatini formalisms, the graviton zero mode in the first model has inner structure when the parameter in this model is larger than its critical value, which is different from the cases of general relativity and Palatini f (R ) gravity. We find that the effective four-dimensional gravity can be reproduced on the brane for both models and the scalar zero mode in the model without a background scalar field cannot be localized on the brane, which avoids a fifth force. Moreover, the stability of both brane systems against the linear perturbations can also be ensured.