In the expanding universe, remote points that are moving away from each other faster than the speed of light (according to their relative recession velocity) are subject to a phenomenon known as cosmological redshift. However, it is important to note that this recession velocity is not a result of objects moving through space faster than light, but rather a consequence of the expansion of space itself.
When it comes to the concept of time dilation, it is crucial to consider the frame of reference from which it is observed. In the context of the expanding universe, if we consider two remote points that are moving away from each other due to the expansion of space, observers situated at those points would perceive time dilation relative to each other.
Due to the expansion of the universe, the space between two distant points is increasing. This expansion affects the measurement of time as well. From the perspective of each point, the other point appears to experience time dilation. This is because the expansion of space stretches the wavelength of light as it traverses the increasing distance between the two points, causing the observed light to be redshifted. Redshift is a result of the stretching of photons' wavelengths, which leads to a decrease in their frequency.
As a result, observers at each remote point would observe the other point's clocks to appear to run slower. In this scenario, the time dilation is not due to relative motion or gravitational effects but is a consequence of the changing space-time geometry caused by the expansion of the universe.
It is important to emphasize that these observations are in the context of the expanding universe on cosmological scales and not related to local motion within galaxies or other gravitational systems, where the effects of time dilation are typically associated with special and general relativity.