The gravity of a very massive luminous celestial object traveling at the speed of light away from us (at the Hubble Sphere) would have an Extremely small, but non-zero gravitation effect on Earth (acceleration). It would be negligible compared to all other gravity, dark energy, etc in our observable universe, but the point of question is zero versus non-zero. Assume the mass is large enough we don't have issues with Heisenberg's uncertainty principle.
If this very massive celestial object was much farther from Earth and traveling away from us much faster such that it was outside our cosmological event horizon (so we would never see any light from it), would the effects of its gravity on earth from it be actually zero, or just an even smaller effect than above?
Benrg, thank you for your point and excellent answer -- wish I were allowed to award 2 correct answers. Yes, the Hubble sphere is not a horizon since gravity fields and light emitted from an object moving at speed c are constantly moving into space with lower escape velocity (oversimplified perhaps). It was used in my question to describe a position far away, but well within the Past Light Cone. To bring this question full circle, my understanding is a massive object outside the Past Light Cone, but inside the Event horizon would have zero effect on Earth, until the specific point in time, t, when the expanding Past Light Cone just barely encompasses the massive object. At which point the full effect of gravity from that massive object (however small) would be felt all at once.