This letter begins with some questions which do not seem to have satisfactory explanations in the current Big-Bang Cosmology. Then it points out a paper [1] which shows that any mechanism which can cause ‘cosmological red-shift’ will also cause ‘time-dilation of super-novae light-curves, so any alternative explanation of the cosmological red-shift’ is not incompatible with the observations of super-novae light-curves. Rather, non-observation of time-dilation in the case of some super-novae needs further works. Then, based on the coincidences noticed by Nobel laureate physicists, and authentic text-books, a derivation is presented showing that every piece of matter and energy is expected to feel the ‘cosmic gravitational force’. This derivation leads to a prediction that not only photons, but all other bodies are expected to feel this ‘cosmic gravitational force’ causing deceleration of their inertial-motion. It is shown that the so called ‘Pioneer-anomaly’ is very much expected based on this derivation.