Constraining an expanding locally anisotropic metric from the Pioneer anomaly Original Research Article

In this work it is discussed the possibility of a fine-tuneable contribution to the two way Doppler acceleration either towards, either outwards a given central mass by considering a background described by an expanding locally anisotropic (ELA) metric. This metric encodes both the standard local Schwarzschild gravitational effects and the cosmological Universe expansion effects allowing simultaneously to fine-tune other gravitational effects at intermediate scales, which may be tentatively interpreted as a covariant parameterization of either cold dark matter, either gravitational interaction corrections. In particular are analysed the possible measurable effects on the outskirts of the Solar system, for heliocentric distances above image, and are derived bounds for the ELA metric functional parameter by considering the bounds on the deviation from standard General Relativity on Schwarzschild backgrounds imposed by the current updated limits for the Pioneer anomaly, taking in consideration both the natural outgassing and on-board radiation pressure, resulting in an average Doppler acceleration outwards the Sun of image. It is also computed the mass–energy density for the ELA metric within the bounds obtained and are discussed the respective contributions to the cosmological density parameter which, for compatibility with the image model, are included in the cosmological relative density of cold dark matter image (image).