Sleep debt is the concept that if you skip half an hour of sleep now, you'll need to catch it up later. I would expect though, that if you skip some sleep, but then start having a normal amount sleep, that gradually your sleep debt would decrease (decay) by itself. Has there been any research on how sleep debt decays?
Very little research exists and over a long period of time it may not even be possible..., the model I work under is this.
If you sleep less than your body would like to, then you pay for it, either you pay for it in terms of more sleep the next day, or you pay for it in terms of lost alertness, creativity, or mood.
Here's the thing - if we were cattle, and all we had to do was eat and stand, then sleep deprivation wouldn't make that much difference to everyday life - similarly if the thing we have to do in a day is travel, then being sleep deprived might not make a difference when all you are doing is sitting on a plane seat for 15 hours.
But if you work in a creative, intellectual, or life-or-death trade, then being 10% off your best can have serious long term implications (junior doctors working on very little sleep are the classic case). I suspect that the trade off isn't this simple but consider it as a question - you can wake up an hour early every day of your life, but you'll be only 95% percent of the person you could be - would you take that choice?
According to the Sleep Docter, you cannot just catch up on sleep. You will eventually return to normal when catching up, but it will take a lot longer than you would generally expect according to a few studies in this aricle.