“Twentica” is episode one of Red Dwarf XI.
The series opens with Lister, Rimmer, Kryten and Cat in Starbug 1 (although they do seem to still have the Red Dwarf; they haven’t lost it again). They detect an unknown ship coming from (really, really) unknown space, and it’s hailing them.
The ship, which is crewed by Simulants (an android species not known for their liking for humans), want to speak to Rimmer. Rimmer is not enthusiastic. However, they are only looking for Rimmer because Lister is under his ‘command’ – Lister rarely obeys Rimmer (who in their right mind would?).
The Simulants are looking to trade something they have for something the Dwarfers have that the latter salvaged off an abandoned Simulant attack ship. Rimmer is opposed to trading with the enemy under any circumstances so, naturally, what the Simulants have is a hostage – Arnold J. Rimmer. It may be another Rimmer, or it may be Rimmer from the future. In the latter case, whilst no-one else would have a problem with the hostage being killed, Rimmer himself does.
The Simulants want something called the Casket of Chronos. Naturally, they are lying about what it does. After the deal is made, the crew find out that what they have traded is part of a time machine, and the Simulants, who are actually Expanoids, want to go back into the past to change the present (Lister makes the first of several comments regarding the use of clichés, and Kryten says that the Expanoids are so unpleasant that they are perfectly willing to use any cliché).
To stop the present from being changed, Starbug 1 hops through the Expanoids time trail, arriving in orbit above Earth. After encountering a field surrounding the planet, which knocks out all the electronics, Starbug crash lands.
They are in the United States, but one in which technology has been made illegal and scientists operate underground. This means, of course, that Rimmer and Kryten are illegal simply by existing. Presumably the banning of technology is down to the Expanoids. So the Dwarfers have to stop the Expanoids using science – and none of them are really that scientific. Kryten is the most proficient, but the others are technologically illiterate.