Long-wavelength corrections to PPN parameters and ?

Mathematics – Logic

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Scientific paper

We consider the problem of an isolated, self-gravitating system embedded in an inhomogeneous universe within the framework of scalar - tensor gravity. The cosmological inhomogeneities are calculated using the long-wavelength iteration scheme. In this scheme the gravitational and matter fields are obtained as expansions in ever-increasing spatial gradients of a `seed' metric. On the other hand, the gravitational and matter fields for the isolated system are obtained to so-called post-Newtonian order. In this paper we write down and analyse the long-wavelength iteration scheme corrections to the PPN parameters 0264-9381/14/5/035/img2 and 0264-9381/14/5/035/img3, as well as 0264-9381/14/5/035/img4, where G is the Newton gravitational coupling. Three different scalar - tensor couplings are considered: (i) the Brans - Dicke constant coupling; (ii) a power-law coupling; and (iii) a logarithmic coupling. It will be shown for all three couplings (with a dust-filled universe) that 0264-9381/14/5/035/img4 decays to the general relativity value of zero. However, the PPN parameters decay to general relativity values only if the scalar - tensor coupling diverges at a fast enough rate.

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