Constraining an expanding locally anisotropic metric from the Pioneer anomaly

► Is computed the gravitational frequency-shift on an anisotropic expanding background. ► Is analysed the compatibility of this frequency-shift with the Pioneer anomaly. ► Are computed the bounds for the functional parameter of this background. ► Are analysed the contributions to the mass-energy cosmological densities. ► It is discussed the possibility of the parameterization of cold dark matter effects