Why would any aliens have any intentions toward us? Why should they care at all? The only resources we have on earth that aren't more easily acquired in space are sitcoms and reality shows.
Even arguably less aggressive and more successful (in terms of longevity) entities such as the British or the Spanish Empire weren't particularly long-lived on a large timescale.
The universe is a big place. Looking around, it seems that the endless-exponential-expansion route hasn’t proven popular with anyone yet. There may just be enough to go around.
It doesn't need to be rational. All it takes is one sufficiently powerful species to decide "better safe than sorry" and lobbing suitable planet killers at any new upstarts they notice.
Now that you know it's there, don't you feel like expending the time, energy, and resources necessary to travel there so you can step on it?
If we could harness all the resources available around the solar system and beyond, we wouldn't have an energy crisis at all. The problem is actually getting those resources transported. If an alien had means to mine and transport resources, they'd probably have found plenty of other richer resources besides Earth.
With our current rate of population growth, I think about one or two percent per year if I remember correctly, we would only make it a few percent across the Milkyway before running out of resources even if we could travel at the speed of light. You can search my comment history, there is somewhere a more detailed comment with all the numbers and assumptions.
Bottom line is, if you want to colonialize the universe, you either need a population growth rate very close to zero and a lot of patience or you have to beat Einstein.
EDIT: Here [1] is the mentioned comment.
For others who like this sort of thing, I highly recommend Isaac Arthur's YouTube channel:
Not disagreeing with your conclusion, but assuming the current rate of population growth is relatively meaningless seeing as no reasonable model assumes current growth rates will continue (as it's been steadily changing).
Unfortunately that is still way too large, to colonialize the Milky Way before hitting resource limits you need it down at one one-thousandth of a percent or so, for the entire universe you need to decrease it several orders of magnitude more. At least on average, if you could use something like cryostasis while travelling through the vast emptiness between stars you could afford times with higher growth rates.
The first drop basically comes because we have a massive population bulge in the post-war years. The growth the resumes because the drop in population growth worldwide is not yet enough to offset the steady growth in life expectancy in the third world.
But longer term that is likely to end up as another bulge.
In terms of developed countries, most have birth rates below replacement.
Once life expectancy growth worldwide has flattened out enough, and birth rates have declined to e.g. European levels, we can expect the bigger problem to be preventing terminal decline. This map [1] is quite interesting. The blue/light blue parts represents birth rates below replacement. In 2015 France too was below replacement.
About half of the worlds population lived in countries with sub-replacement birth rates as of 2010, and despite the fact that the population growth tilts that towards high population growth countries on a continuous basis, the birth rates of those countries is dropping pretty much across the board, meaning it is likely that the proportion of the worlds population living in sub-replacement countries will actually increase.
E.g. India is expected to drop below replacement this century too, and actually experience population decline (decline lags birth rates, of course, because you need to wait for the generation that's dying off to be larger than the one being born).
So I don't think population growth is a realistic concern when it comes to interstellar exploration. On the contrary.
[1] https://en.wikipedia.org/wiki/Sub-replacement_fertility#/med...
Our population isn't expanding exponentially. World population grew at 2%/yr in 1960, 1.55% in 1995, 1.25% in 2005, 1.18% in 2015, 1.14% in 2016, and 1.12% this year.
Soon every person we send off the planet will just reduce earth population by 1. We'll be lucky if people reproduce enough to keep the population steady.
But current projections is a population in the region of 10bn first by the end of the century, with some projections suggesting population decline from as early as 2040 (though that's an outlier). More scenarios predict a peak in the 2070-2100 timeframe; some predict continued, but much reduced growth beyond 2100. As far as I'm aware, though, all reasonable scenarios suggest that the rate of growth will at the very least continue to slow for a long time.
That looks pretty exponential to me. If it no longer looks exponential when looking at the last few years perhaps it's because we're running into resource limits.
It's true that animal populations peak (s-curve) when they hit resource limits (ie: carrying capacity of the environment). But our population has slowed because of education (in particular, education of women)... it's an effect thats been repeated all over the world.
If it were resource limits, we would see things like famine (killing the excess members of the population), rampant disease (which becomes easier to spread when people are closer to each other), etc. We're definitely not there in the developed world; and the 3rd world isnt there either, since they have some of the highest reproductive rates.