Physics > Economics The Do The Math blog by Caltech-trained UCSD astrophysicist Tom Murphy is the best resource in this area. In particular the posts - Galactic Scale Energy https://dothemath.ucsd.edu/2011/07/galactic-scale-energy - Can Economic Growth Last? https://dothemath.ucsd.edu/2011/07/can-economic-growth-last - The dinner conversation with an economist on this topic https://dothemath.ucsd.edu/2012/04/economis…
His energy analysis concluded that at 2.3% growth rate and current technology, we would need to use the entire energy supply falling upon the earth's surface within 275 years. Improving technology might be able to stretch that to 400 years. Within 1400 years, we would need to use the entire energy of our solar system.
But we have a number of more pressing demographic constraints. As countries develop, fertility falls; fertility rates are currently below replacement in the entire developed world [1] with all regions other than Africa falling below replacement rate by 2050. Within 80 years, population is likely to start falling, with some studies predicting this within 30 years. Worse, there's a worldwide demographic bulge of 18-30 year old males that's hitting just about now; such demographics have been associated with a higher likelihood of war in the past.
There's plenty of other problems that these bring: if you don't get killed in war and manage to find a mate, you're not likely to see your social security or 401(k) worth all that much, nor will you find health care unless your rich or lucky or both. But they'll happen way before we reach physical limits on growth. Our threat model should be stupid politicians doing stupid things at the behest of frustrated populations, not the laws of physics.
[1] http://worldpopulationreview.com/countries/total-fertility-r...