In my comic, there is no conventional true "time travel" as the past cannot truly change: however, consistency between the continuity of past, present and future relies on the current Living Universe "remembering" what happens to and in it. When the Universe dies, some of these Memories are used as a foundation for a new Living Universe while the rest of the Memories that are deemed irrelevant are left behind to be forgotten.
The main conflict happens when these Memories find a way to personify and maintain themselves before they can become truly forgotten, and force the current Living Universe's Reality to be more similar to the Reality of the Dead Universes that they originated from. Since there is no real way for them to change the actual events of the past, they instead change the way the past is remembered so that the Universe is forced to realign the present to be "consistent" with what it believes is the past.
Of course, doing this repeatedly over time erodes the Reality of the Living Universe itself when it begins to "realise" that the past and present don't 100% align and the number of inconsistencies and plot holes increase, which messes up their potential to reach the future lol