I remember when I started doing global system models on, among other, the population size. One of the first realizations I had was that the cure for cancer everyone is hoping for might have serious consequences on the population size. Back then it was already somewhat clear to me that we were probably above the carrying capacity, meaning that the planet biophysically couldn't sustain life for even the current population. Sustain as in the "long" run.
Overshooting the carrying capacity is pretty common in biology. A classical example in ecology is a group of sheep and a group of wolves both living in the same area. If the number of wolves becomes too high, they will eat more sheep, meaning that the sheep have fewer offspring. That will limit the number of sheep, leading to less food for the wolves. Then the wolves start dying from starvation, leading to a drop in their population size. That leads to fewer sheep being eaten, and therefore their population grows. All in all, in that example it seems to balance out through negative feedback loops, but the first part of the story is that there are too many wolves, meaning that their population size overshot their carrying capacity.
The whole biosphere is a LOT more complicated than that, but looking at humans, we have used external energy to boost our food production (internal energy). During the green revolution, we have started using artificial fertilizers (you need energy to mine, refine and produce those), and we've started using machines like tractors and harvesters in the global agriculture. That is fine and dandy it seems, because it has reduced the global hunger and malnutrition, but because we use energy in a way that is seriously non sustainable it should "raise an eyebrow". The more I modelled, the more it became clear to me, that we are way above the carrying capacity. I honestly don't know what the carrying capacity really is, but to the best of my knowledge it is somewhere between 1-4 billion, depending on how we use resources. With the way we currently behave, it's closer to 1 than 4.
Realizing that scared the crap out of me on behalf of the young generations, because no matter how eco friendly humanity becomes, it seems that we are still high above the carrying capacity, and you don't need to study much ecology to get to know the inevitable consequences of that. We can make all the modifications to the telomeres etc. we want, it won't ensure that immortality everyone seems to long for. There simply ain't food enough already, and if we lower the death rate then the overshoot of the carrying capacity will just become more, how shall I put it... "violent".