Each of these chapters takes place in their own separate AUs. These stories are not related to each other in any way. Everything was written before S4 aired.
Father Time
Touching the time core is not advisable, even if it is your last resort to temporarily stun a time demon. As expected, Rip Hunter blew himself to pieces to slow down this demon. Everyone assumed him dead. Yet, something remarkable happened: Rip's consciousness survived.
Of course, since this event is extremely rare, nobody thought of this possibility. His dormant consciousness only existed in the intangible concepts of time and space. Slowly, he attracted particles. His brain became tangible, and he regained his former shape. This process was painstakingly long, but it was worth it. Rip had a functional body again, and he gained so much more. The time energy, released during the explosion, had embedded itself in his body.
Interesting side-effects manifested. He was everywhere, and nowhere at once. He saw all that ever was, is, and will be. With one thought, he traveled anywhere and anytime. He visited many time period, the duration of his stay varying between a couple of hours and a millennium. He witnessed the fall of Rome and the rise of the Kasnia Conglomerate. Never speaking, ever in the shadows and every so often, nudging the world in a particular direction. He never outright grabbed power – he did not need power – but he patiently aided some important political figures to bring the course of humanity back on track.
Conspiracy theories about a mysterious man spotted near world leaders always amused him. He did not shy away from fueling them, either. As rumors spread, more people joined in the conversation. This is the only conspiracy theory that withstood the test of time and stayed within public memory.
Around the 25th century, he caused all religions to go extinct but one: his own. They personified him as Father Time, and all people believed. They were accurate in the personification, and he thought it was about time humanity worshiped him like the deity he had become.
He no longer referred to himself as "Rip Hunter". He forgot the Legends and his family. He hungered for their praise – there aren't many other ways to feel truly alive. He returned to different time periods and imposed Himself as a god, to make His position stronger and eternal. The more changes He made to satisfy His needs, the sooner His religion became the dominant religion in the future, and the more His religion looked like a cult; they followed the principles to the letter and never strayed.
However, unconsciously, he never returned to the moments where the Legends had been. He did not wish to interfere with the course of their history – He only became a god because of their involvement, after all. They did notice His changing the timeline, and they tried to stop him. They did not stand a chance.
His work was finished. He traveled to the year 2845, at the peak of the religious zeal, and presented Himself to the people. They promptly crowned Him their eternal ruler after His display of powers.
He sits on a marble throne in the tallest building. He has servants answering to His every whim, and every year on the day of His coming to Earth, the people of each district sacrifice one human life for him. He watches, smiles, and tells them He is pleased. Enemies are still plentiful, but with the biggest show He can give, He strikes them down and prolongs their deaths and suffering so He can listen to their begging, then removes them from the timeline.
Let it be known that Father Time is not a benevolent god. His attention and protection must be earned, and His scorn does not differentiate between friend or foe. Do not cross him if you value your life, for he will make it so that you are never born