A heuristic solution for the Pioneer anomaly employing an ELA metric with dark matter in the outskirts of the Solar system

Abstract: Considering an expanding locally anisotropic (ELA) metric with the Sun as central mass and the heuristic ansatz for the dimensionless functional exponent parameter 'alpha=3+alpha_2(r_1)(1-U_Sun)^2' with a linear ansatz 'alpha_2(r_1)=alpha_2^2.0+alpha_2^2.1 r_1' above 20 AU the pioneer anomaly is fully accounted for as due to the blue-shift of the background space-time. For compatibility with orbital motion within the Solar system it is further considered a branch ansatz for which \alpha_2(r_1)=0 below 20 AU. This construction reduces the physical acceleration correction above 20 AU down to ~10^-14 m/s^2 outwards from the Sun such that orbital corrections to Neptune and Pluto are less notorious than when the full Pioneer acceleration is considered to be a gravitational acceleration. It is also discussed the effective mass-energy density distribution above 20 AU due to the background corrections, the respective equation of state ('-1 < w < -0.726') and the finite non-null total mass is computed by considering an upper cut-off for the functional parameter 'alpha'. Such effective extended configuration is tentatively interpreted as a cold dark matter distribution.