Generalised Boundary Terms for Higher Derivative Theories of Gravity
  In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity. 
Ali Teimouri, Spyridon Talaganis, James Edholm, Anupam Mazumdar
gr-qc