To put some numbers on it, at a 1% growth rate starting with the current population in around 12100 the volume of space we could theoretically have access to (a

To put some numbers on it, at a 1% growth rate starting with the current population in around 12100 the volume of space we could theoretically have access to (a sphere with a radius of 12100 light years), the amount of volume available per person would be under 0.06 m^3, which is what the Internet tells me is the volume of a typical human. Of course we couldn't get anywhere near that, because that 12100 light year radius sphere doesn't contain enough mass to make that many humans. At 1% annual growth here are some of the mass bottlenecks we'd hit. 3400 years for the mass of living humans to equal that mass of the Earth and Moon. 600 years after that we would equal the mass of Jupiter. 700 more years and we equal the mass of the entire solar system. 2000 years after that (or 6700 years from now) we'd need the entire mass of the Milky Way to make those humans. From there it is just another 100 years until we need the mass of the Andromeda galaxy. Another 5500 years (12300 years from now) and we'd need the mass of the entire observable universe.