HAMILTON-JACOBI EQUATION FOR BRANS-DICKE THEORY AND ITS LONG-WAVELENGTH SOLUTION

The Hamilton-Jacobi equation for the Brans-Dicke theory is solved by u sing a long-wavelength approximation. We examine the non-linear evolut ion of the inhomogeneities in the dust fluid case and the cosmological constant case. In the case of dust fluid, it turns out that the inhom ogeneities of space-time grow. In the case of cosmological constant, t he inhomogeneities decay, which is consistent with the cosmic no hair conjecture. The inhomogeneities of the density perturbation and the gr avitational constant behave in a manner similar to those of space-time .