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The success of the S-matrix in quantum field theory in Minkowski spacetimenaturally demands the extension of the construction of the S-matrix in ageneral curved spacetime in a covariant manner. However, it is well-known thata global description of the S-matrix may not exist in an arbitrary curvedspacetime. Here, we give a local construction of S-matrix in quantum fieldtheory in curved spacetime using Riemann-normal coordinates which mimics themethods, generally used in Minkowski spacetime. Using this construction, thescattering amplitudes and cross-sections of some scattering processes arecomputed in a generic curved spacetime. Further, it is also shown that theseobservables can be used to probe features of curved spacetime as these localobservables carry curvature-dependent corrections. Moreover, the compatibilityof the local construction of the S-matrix with the spacetime symmetries is alsodiscussed in detail.

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