Higher Derivative Theory for Curvature Term Coupling with Scalar Field

Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most second derivatives of scalar field non-minimally coupled to curvature terms. Here we perform (3+1) decomposition Lagrangian separate time form the rest. is useful check hidden will help us find conditions under which instability do not appear. In our case, no non trivial stop appearance ghost.