Yes, according to the theory of general relativity, time dilation occurs in deep space. Time dilation is a phenomenon where time passes at different rates depending on the strength of the gravitational field or the relative velocity between two observers.
In deep space, away from massive objects like planets, stars, and black holes, the gravitational field is relatively weak. As a result, time dilation in deep space is mainly caused by relative velocity. When an object moves at high speeds relative to another observer, time for that object appears to pass more slowly from the perspective of the stationary observer.
This effect was famously demonstrated by the twin paradox thought experiment. Imagine two identical twins, where one twin remains on Earth while the other travels to deep space in a high-speed spacecraft and returns. The traveling twin will have experienced less time compared to the twin who stayed on Earth due to their relative velocity. This difference in the passage of time is an example of time dilation.
So, in summary, both gravitational time dilation and relativistic time dilation (caused by relative velocity) can occur in deep space. However, in deep space, gravitational time dilation is generally less significant compared to regions closer to massive objects.