CONSTRAINING MODELS OF MODIFIED GRAVITY WITH THE DOUBLE PULSAR PSR J0737-3039A/B SYSTEM
Abstract
In this paper we use ΔP = -1.772341 ± 13.153788 s between the phenomenologically determined orbital period Pb of the PSR J0737-3039A/B double pulsar system and the purely Keplerian period 
calculated with the system's parameters, determined independently of the third Kepler law itself, in order to put constraints on some models of modified gravity (f(R), Yukawa-like fifth force, MOND). The major source of error affecting ΔP is not the one in the phenomenologically measured period (δPb = 4×10-6s), but the systematic uncertainty δP(0) in the computed Keplerian one due to the relative semimajor axis a mainly caused, in turn, by the errors in the ratio 
of the pulsars' masses and in sin i. We get |κ| ≤ 0.8 × 10-26m-2 for the parameter that in the f(R) framework is a measure of the nonlinearity of the theory, |α| ≤ 5.5 × 10-4 for the fifth-force strength parameter (for λ ≈ a = 0.006 AU). The effects predicted by the strong-acceleration regime of MOND are far too small to be constrained with some effectiveness today and in the future as well. In view of the continuous timing of such an important system, it might happen that in the near future it will be possible to obtain somewhat tighter constraints.
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