There is a standard formula for gravitational time dilation used in eg the operation of the global positioning system. It is based on the integration of g(h) where g is a function relating gravitational force (acceleration if you prefer) to h, height. But I can't see any way of applying this to the universe as a whole; there is no parameter equivalent to h, the height, and in any case the force of gravity, on the very large scale, is not only the same everywhere, it is actually zero.
This seems to mean there is no large scale time dilation in the universe, as you look back in time, though I have heard that gravitational time dilation does contribute to red shift. The gravitational field or potential does increase as you look back in time and the universe is more dense, but it is uniform, leading to no force. So a different formula is required, based on gravitational potential, not force, if one exists.
