Constraining the cosmological constant and the DGP gravity with the   double pulsar PSR J0737-3039
  We consider the double pulsar binary system as a laboratory to locally test the orbital effects induced by an uniform cosmological constant $\Lambda$ 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=Delta\dot\omega/Delta P of the discrepancies between the phenomenologically determined periastron rate \dot\omega and orbital period and their predicted values from the 1PN approximation and the third Kepler law. Then, we compare its value R = (0.3 +/- 4) \times 10^-11 s^-2, compatible with zero within the errors, to the ratios R_Lambda and R_DGP of the effects induced on the apsidal rate and the orbital period by Lambda and the DGP gravity; we find them neatly incompatible with R being R_Lambda = (3.4 +/- 0.3) \times 10^-8 s^-2 and R_DGP = (1.4 +/- 0.1) \times 10^-7 s^-2, respectively. Such a result, which for the case of Lambda 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. 
Lorenzo Iorio