Gravitons radiated (due to expansion of space) by celestial bodies interact with space producing slower expansion. If time (Motion and Forces) is due to the expansion (stretching) of space then time will slow with slowing of expansion. Gravitational acceleration is the result of time differential and does not slow time as commonly believed. Einstein's equivalence principle which compares gravitational acceleration to accelerated motion may give an incorrect impression that slowing of time is related to acceleration. This is not true. Acceleration gravitational or otherwise does not cause time dilation. This is discussed in more detail under acceleration and twin paradox.
Expansion of space imparts motion and forces that is equal to the total energy in a given mass. Let us consider that the amount of energy i.e. total motion and forces imparted by expansion of space is a constant = MC^2.
Keeping this in mind let us see what happens when an object is accelerated. To increase the velocity of an object we have to apply force. The force changes the way space acts on that object. The object interacts with space and the expansion of space slows in front of object and becomes faster behind the object. As time is related to expansion of space this sets up a time differential with slower time in front of the object and faster time behind perpetuating the motion. The objects moves in time differential from faster to slower time. This also beautifully explains the real mechanism of length contraction
Now the expanding space is causing this mass to move linearly as well. The total amount of motion (imparted by the expanding space) to an object is a constant, therefore as the external or linear motion increases the internal motion of atoms and the forces decrease proportionally. The reduced internal motion is the observed slowing of time. The force applied to accelerate the object only increased its mass. This observation is clearly supported by the equations of motion.
The above concepts are precisely mathematically correct. For more information contact the author.