I'm imagining a near-future world where a process can be undergone that will halt all future aging of the body, but the approach causes infertility. Those undergoing it will not have (biological) children afterwards. This means that the long life does not lead to exponential growth in population, as the number of new children per generation has not increased by the extended life span. In fact since some may choose to undergo the anti-aging process when younger, to ensure they live their life in a younger more youthful body, the choose to self-sterilize by going through anti aging process may in fact drop the total birth rate per generation slightly.
These no longer aging adults will obviously not die of old age. Our medical technology will also increase and so death from health issues like heart disease or cancer will also decrease by a good amount (though some will still happen). However, death by accidental, homicide, suicide, etc will still occur slowly leading to the adults with expanded life span still eventually dying.
I'm wondering how much this will expand the total world population relative to today. Obviously with so many people living longer our total population will go up. However, at some point we would still hit equilibrium, where the number of deaths via non-age related causes will still equal the number of births.
I'm looking primarily at first world nations when it comes to population growth and total population size. Keep in mind many first world nations of today already have stable or decreasing population size if one ignores immigration, ie they don't birth as many children as adults die.
For now I want to assume that the increased population does not lead to a significant resource limitation putting constraints on birth rate or survival; ie were not all fighting over limited food/space caused by doubling our population. I'll be considering resource limitations in future questions based off of the answer to this one. However, Our population has time and time again doubled past what people thought would be an unsustainable population thanks to technology allowing more efficient production of food and usage of resources etc so it's possible our technology alone will be able to sustain the increased population well, but I'm also not beyond adding limited emigration to new worlds to make up for a situation where the population is just too high.
I'd also mostly like to ignore options such as freezing eggs prior to undergoing the anti-aging process or similar approaches to work around the infertility issues. I'll address such potential later, it may even be that such approaches are outlawed (or heavily regulated/taxed) by governments to help ensure sustainable populations.
I'm looking for hard science answers, if you can actually point to studies to back up claims on things such as birth rates and death rates I'd love it (though I don't require it).