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Abstract

In the frame work of TREDER's gravitational theory we consider two classes of field equations which are derivable from two classes of LAGRANGEian densities Ω(1)1, ω2), Ω(2)(s̀1, s̀2). ω1, ω2; s̀1, s̀2 are parameters. Ω(2)1, ω2) gives us field equations which are up to the post-NEWTONian approximation in the sense of NORDTVEDT, THORNE and WILL equivalent to the field equations given by BRANS and DICKE. For ω2 = −1 −2ω1 field equations follow from Ω(1)1, −1 −2ω1) which are in the above mentioned sense of post-NEWTONian approximation equivalent to EINSTEIN's equations. The field equations following from Ω(1)1, ω2) have a cosmological model with the well known cosmological singularities for T [RIGHTWARDS ARROW] ± ∞ in case that ω1/(1 +3ω12) [TRIPLE BOND] γ > 0. For ω1/(1 +3ω12) ≤ 0 cosmological models with no cosmological singularities exist.

From Ω(2)(s̀1, s̀2) we obtain field equations which at the best give us perihelion rotation 7% above EINSTEIN's value and light deflection 7% below the corresponding EINSTEIN's value. But in that case we are able to show the existence of a cosmological model without any cosmological singularity.