A common supposition about time travel is that if it were possible, all of time and space would be glutted with evidence of it--not just time travelers themselves, but anachronism of all sorts.
If it is possible but the evidence is not ubiquitous, then this is caused by physical rules which limit the impact of time travel, some form of intelligent authority mitigating the effects, or both.
The Department of Chronal Affairs was formed to investigate temporal anomalies in the first place. They weren't empowered to do anything about them. Their mandate was solely to observe and report. It was once they began to grasp the full scope of the damage being caused by time travel that they transformed into the Chronal Authority, and the name was hardly an understatement. A multispecies effort to reduce the deleterious effects of time travel, their mission was broad and deep. First, you have to understand a little bit about how time travel works in the first place.
In our universe, "time travel" as such doesn't exist. There is no single timeline that a person can go backward in to a specific period in the past and then start time's arrow moving forward from that point. Instead, a journey into the past creates a new timeline from that point forward. (Note that traveling back to the future has no such effect.) The implication here is that every single journey taken by a time traveler into the past produces a whole new timeline, thus the quantity of timelines is essentially limitless. A time traveler could then be thought of as a person traveling laterally between different timelines. If you travel through time to produce a specific result, an equally valid way to think of it is that you are searching for a specific timeline.
There are then three types of timelines: those created by time travelers which have the invention of time travel in their past or future; those created by time travelers from a point prior to the invention of time travel, and which never invent it; and the original or "prime" timeline. The third is impossible to locate or travel to--you would simply have to have been born in it, and you'd never know in the first place--and the second type of timeline is irrelevant, as it constitutes a single line that ends. It is the loops of time travelers creating additional timelines, over and over, that particularly concern the CA.
Now, that is exactly the sort of thing I do, so I have to watch myself, or so I've been warned. I don't dispute their reasoning. For a crude analogy, consider a photocopier. You can copy an original document and it will look pretty close. If you start copying the copy, and copy successive generations of copies, you lose fidelity and eventually you start to lose vital information. Primitive methods of cloning lifeforms have the same problem, though their degradation starts earlier. For reasons no one has been able to ascertain, timeline creation operates similarly. The more divergence points a timeline has from the prime timeline, the greater its potential instability. One of the dirty secrets of time travel is that sometimes you create a branch that is critically unstable, meaning it destroys itself the moment it's created. Most forms of time travel technology cannot cope with this and the errant traveler un-exists right along with the rest of the timeline. Some are minimally stable in that a recognizable universe exists, but perhaps a physical constant has been copied just slightly incorrectly, so the universe is immediately incompatible with life. Obviously, the effect is the same as the preceding scenario. You could imagine various forms of instability that would result in very rapid or very slow unraveling of the physical basis of a timeline, and virtually all of those have been encountered or at least theorized.
The CA cannot do anything to save these doomed timelines. Time travelers who inadvertently create them and die along with them are saving the CA the trouble of apprehending them, too. What the CA concerns itself with are timelines which can be saved, and in particular, those which can be causally merged to reverse some of the replicative degradation. How they do this is a closely-held secret, though a basic version of this technology exists with the Sikaren timeships. It should be noted that doomed timelines also seem to affect adjacent ones. The main effect appears to be rifts in spacetime that open and close randomly, swallowing up anything nearby. Not a big deal in most of the universe, since it is empty, but nobody is too happy when an entire populated planet disappears into the maw of a time-rift. That's a bad day at the office if I ever heard of it.
All of that is perhaps a bit grandiose. Much of the CA's job is akin to traditional law enforcement. Time travelers create irritating problems in the timelines they spawn, victimizing innocent people, and the CA works to apprehend them.
Simple theft is one of the most common "time crimes." What collector wouldn't want a pristine ancient artifact in his collection? The solution to that is straightforward in most cases: the object in question is retrieved and put back where and when it belongs. Sometimes CA agents address it by traveling to just after the thief's arrival in the past, stopping the theft in the first place, and taking the traveler with them. Although such an endeavor spawns at least two new timelines, the CA believe that since their actions create a very brief window of temporal anomaly, that the timelines all causally merge back to their original timeline. There is at least some evidence they are correct, though I cannot claim to understand the mathematical proofs they offer for it. The timeline in which the theft was originally successful does endure and I have never seen a satisfactory explanation for how those can be addressed--the CA seem to simply handwave it.
Another temporal violation is fraud. There are many, many forms of fraud, but when it comes to time travel the main type is duping someone in the past for your own personal gain. This could mean promising them something you won't deliver, giving them something that isn't what you claim it is, and so on. Some forms involve handing over a valuable item to the victim and then coming back later to steal it. They can't exactly press charges against someone who fucked off to 1000 years in the future, can they? The CA preemptively handles these cases as much as possible, too.
You might think murder is one of the harder crimes to deal with, but the overwhelming majority of the time the CA will simply thwart the murder just before it occurs, attempting another causal convergence. Yawn. Nothing new to see here.
The trick with most of these crimes is that detection is easy. An object identifiable from a specific time and place is self-explanatory. You know exactly where it was stolen from and thus where it needs to be returned. Frauds and murders are also relatively easy to trace back to their origins. The really difficult cases are the ones where the exact origin is almost impossible to place, especially instances where the perpetrator has gone out of their way to avoid detection.
A certain type of temporal prankster, for instance, likes to go around inventing religions and other arbitrary belief systems, sometimes promoting them at different points in time and aiding their spread. This can be done in such a way that it's difficult to know exactly when and where it began; you could perhaps narrow it down some, but if it's seeded effectively you'd almost never be able to catch the person who did it and stop them from polluting a timeline with bogus beliefs. I hear this normally isn't even done for any kind of self-aggrandizing or profitable motive, some just enjoy wreaking havoc with people's souls.
Theosophy might be my personal favorite scam of this nature. What if every religion was kind of true and you just smashed them all together and claimed to have access to a plane of existence containing the complete knowledge of all that could ever exist? If such a thing existed, I am certain at least one of the many obnoxious alien races I've encountered would have found it and would have proceeded to never, ever shut up about it. The CA, for their part, have never figured out who was behind it. Their working hypothesis is that it was a disgruntled former agent as some of the details align neatly with CA policies and practices. There is something a bit goofy about a rogue time cop going back in time and turning being a time cop into an esoteric religion. I appreciate the chutzpah, myself.
The less said about my own encouters with the DCA and the CA, the better. They don't like me, I don't like them. We operate at cross-purposes. My understanding is they've captured a bunch of versions of me over the years, but the one telling this story has thus far gotten away with it. It was once confided in me by the Director of Chronal Affairs that there exists an ultimate penalty for the worst offenders, people who do things like travel through time solely to perpetrate heinous, large scale crimes, or who intentionally generate huge quantities of timelines in order to experiment with the failure modes of the universe for unthinkably sinister purposes. You see, every timeline in which time travel is invented ultimately concludes at the final point in spacetime. This may not be at the same calendar date, as such, for each timeline. But they all join together at this fixed point nonetheless, where all causalities collapse into a single, fateful end. It is here that the CA operate a facility outside the boundaries of time and space, and it is from here that they are able to trace through every single timeline in which an individual exists and intentionally collapse them through what they call a "causal inversion." No one is allowed to know exactly what that is, either, only that it ensures an especially dangerous individual is erased from all of existence, permanently. The only place any record of them will survive is aboard the facility, the End Point.
By definition, I don't know of anyone this has happened to. It would be a grievous breach of protocol for information about any such individuals to be shared with me, no matter how much the Director likes me personally. (I think he likes me, anyway.) I have been told in no uncertain terms that no one is above having the so-called "failsafe protocol" used against them, however. To make the point, I'm told more than one rogue CA agent has had it done to them. Truly, no one is immune.
Lucky for me, I've still got a warning left before I start to get in any real trouble!