Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate

The success of the S-matrix in quantum field theory in Minkowski spacetime naturally demands the extension of the construction of the S-matrix in a general curved spacetime in a covariant manner. However, it is well-known that a global description of the S-matrix may not exist in an arbitrary curved spacetime. Here, we give a local construction of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinates which mimics the methods, generally used in Minkowski spacetime. Using this construction, the scattering amplitudes and cross-sections of some scattering processes are computed in a generic curved spacetime. Further, it is also shown that these observables can be used to probe features of curved spacetime as these local observables carry curvature-dependent corrections. Moreover, the compatibility of the local construction of the S-matrix with the spacetime symmetries is also discussed in detail.