It is clear that energy consumption cannot continue to grow exponentially for much more than 1000 years. But it might be argued that we can continue to extract ever more economic value from less and less energy, especially with VR. This is discussed in the debate between Robin Hanson and Bryan Caplan, and Toby Ord in the comments. 

See the comment here by Max Daniel:

"there are limits in how much value (whether in an economic or moral sense) we can produce per unit of available energy, and (ii) we will eventually only be able to expand the total amount of available energy subexponentially (there can only be so much stuff in a given volume of space, and the amount of available space is proportional to the speed of light cubed - polynomial rather than exponential growth).

...

And:

In 275, 345, and 400 years, [assuming current growth rates of global power demand] we demand all the sunlight hitting land and then the earth as a whole, assuming 20%, 100%, and 100% conversion efficiencies, respectively. In 1350 years, we use as much power as the sun generates. In 2450 years, we use as much as all hundred-billion stars in the Milky Way galaxy.

(Tom Murphy)

 

TL;DR: It seems that Metaculus forecasters believe there is at least a >16-23% chance that our solar system could sustain an economy of at least 10^11 trillion 2020 USD, i.e. one billion times larger than the world economy today.

(This is a lower bound based on what Metaculus thinks there is a 16-23% chance of actually happening by 2200, and assuming that our solar system only accounts for 1/10,000th of the economy that Metaculus thinks will exist with that probability.)

On what basis do I make this inference?

19 forecasters on Metaculus currently give a 16% chance of GWP in 2200 being > 10^15 trillion 2020 USD:

12 forecasters on Metaculus (overlapping with the above 19) currently give a 23% chance of GWP in 2200 being >10^15 trillion 2020 USD (on this "big range" version of the question):

This roughly translates to a >16-23% chance that our solar system could sustain an economy 

Such an economy might span roughly 10,000 stars if we have a fast takeoff scenario by 2050 and start colonizing our galactic neighborhood at near the the speed of light.

Naively then I'll say that 1/10,000th of such an economy would be contained within our solar system to calculate a lower bound on how large our solar system's economy can get:

It therefore seems that Metaculus forecasters believe there is at least a >16-23% chance that our solar system could sustain an economy of at least 10^11 trillion 2020 USD, i.e. one billion times larger than the world economy today. (This is a lower bound based on what Metaculus thinks there is a 16-23% chance of actually happening by 2200, and assuming that our solar system only accounts for 1/10,000th of the economy that Metaculus thinks will exist with that probability.)

 

In Holden Karnofsky's just-published Cold Takes blog post This Can't Go On, he cites how at 2% annual economic growth the economy would grow by a factor of 3*10^70 in just 8,200 years. Since there are likely fewer than that many atoms in our galaxy, this would mean that "we'd need to be sustaining multiple economies as big as today's entire world economy per atom." Holden says:

Is it imaginable that we could develop the technology to support multiple equivalents of today's entire civilization, per atom available? Sure - but this would require a radical degree of transformation of our lives and societies, far beyond how much change we've seen over the course of human history to date. And I wouldn't exactly bet that this is how things are going to go over the next several thousand years.

It seems much more likely that we will "run out" of new scientific insights, technological innovations, and resources, and the regime of "getting richer by a few percent a year" will come to an end. After all, this regime is only a couple hundred years old.

(Edited 8/3 to include the written post quote now that it's published, rather than my transcription of the audio)

This seems relevant: https://www.overcomingbias.com/2009/09/limits-to-growth.html