Constraining the cosmological constant and the DGP gravity with the double pulsar PSR J0737-3039

We consider the double pulsar PSR J0737-3039A/B binary system as a laboratory to locally test the orbital effects induced by an uniform cosmological constant Λ in the framework of the known general relativistic laws of gravity, and the DGP braneworld model of gravity independently of the cosmological acceleration itself for which they were introduced. We, first, construct the ratio R=Δω˙/ΔP of the discrepancies between the phenomenologically determined periastron rate ω˙ and orbital period Pb and their predicted values from the 1PN ω˙1PN approximation and the third Kepler law P(0). Then, we compare its value |R|=(0.3±4)×10-11s-2, compatible with zero within the errors, to the ratios RΛ and RDGP of the effects induced on the apsidal rate and the orbital period by Λ and the DGP gravity; we find them neatly incompatible with R being RΛ=(3.4±0.3)×10-8s-2 and RDGP=(1.4±0.1)×10-7s-2, respectively. Such a result, which for the case of Λ is valid also for any other Hooke-like exotic force proportional to r, is in agreement with other negative local tests recently performed in the Solar System with the ratios of the non-Newtonian/Einsteinian perihelion precessions for several pairs of planets.