Future Histories And Time Travel

(Most of today so far has been spent driving back to Lancaster.)

Robert Heinlein
Heinlein's Future History was complete in five volumes but unfortunately he added three or four inauthentic novels. The first of these, Time Enough For Love, concludes with a time travel section, "Da Capo," that includes an ingenious passage on how Lazarus Long sends messages home from the early twentieth century but otherwise is appalling drivel. (I go further and add that at times Heinlein's later obsession with sex became frankly offensive.)

Isaac Asimov
Asimov's The End Of Eternity is an incoherent time travel novel (see here) that concludes by initiating the timeline of his Galactic Empire future history.

Poul Anderson
Anderson did not connect the Time Patrol to the Technic History but did connect There Will Be Time to the Maurai History.

However, in the Technic History, two characters present the germ of a time travel story. See here. Let us expand it:

the Marchwardens of the Lauran System have reason to expect an attack from the future and prepare defenses;
the attack arrives and is defeated;
five centuries later, the Merseians have a time machine and consider attacking the Lauran System five centuries earlier;
however, historical records inform them that that attack arrived and was defeated;
therefore, they do not launch the attack.

By the Time Patrol rules of time travel, this could happen. The cancellation of the launch of the attack cannot prevent the earlier arrival of the attack.