Is there gravitational time dilation as we look further out into space (and therefore further back in time)?

Question

There is a formula for gravitational time dilation which relates the slowing of time to a changing force of gravity.

                      h
Td(h)  =  exp[1/c^2   ʃ  g(h) dh]   
                      0

The force of gravity is due to the gradient of a gravitational field. But in the universe, if spatially flat, at a universal scale, the gravitational field is constant (uniform). With no gradient there is no force of gravity and hence no gravitational time dilation.

But as we look further out into Euclidean space, we are looking further back in time to a time when the universe was more dense. Presumably, in the older universe, the gravitational field, though still uniform, becomes stronger. Does a stronger gravitational field lead to time dilation even though there is no force of gravity? If so, to calculate it would require a different formula. Does one exist? And if so, how does the calculated time dilation compare to the measured red shift? (Red shift can be explained as time dilation).

Answer 1

If space is not Euclidean, the universal gravitational field will not be uniform and there will be an associated force of gravity, which allows the above formula to be used to calculate time dilation as we look further out into space.

This would seem to be correct, but if so, I think the force of gravity would only express itself in the direction of time.