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Non-local theories of gravity are considered extended theories of gravity,meaning that when the non-local terms are canceled out, the limit of GeneralRelativity (GR) is obtained. Several reasons have led us to consider thistheory with increasing interest, but primarily non-locality emerges in anatural way as a side effect of the introduction of quantum corrections to GR,the purpose of which was to cure the singularity problem, both at astrophysicaland cosmological level. In this paper we studied a peculiar case of the socalled Deser-Woodard theory consisting in the addition of a non-local term tothe Hilbert-Einstein lagrangian, and we derived for the first time contraintson the dimensionaless non-local parameter A by exploiting the predictedgravitational wave emission in three binary pulsars, namely PSR J1012+5307, PSRJ0348+0432 and PSR $J1738+0333. We discovered that the instantaneous fluxstrongly depends on A and that the best constraints (0.12 < A < 0.16) come fromPSR J1012+5307, for which the GR prediction is outside the observationalranges. However, since for PSR J1012 + 5307 scintillation is suspected, asemerged in a recent census by LOFAR, corruptions in pulsar timing could behidden. We finally comment on the usability and reliability of this type oftest for extended theories of gravity.

Constraints on non-local gravity from binary pulsars gravitational emission