For a brief introduction to his research, see "How Many People Can the Earth Support?" https://www.nybooks.com/articles/1998/10/08/how-many-people-...
Paywall: https://archive.is/E5AB8
He makes a much more complete exploration in his 1995 book, How many people can the earth support?, Cohen visits many estimates and/or claims regarding carrying capacity and explores the assumptions or logic behind many of these, which range from a low of about 100 million to highs over 12 trillion. Most such estimates cluster around 1--10 billion, and seem more credible than outliers, especially of the high-end group.
https://www.worldcat.org/title/how-many-people-can-the-earth...
https://archive.org/details/howmanypeoplecan00cohe
There are also a few articles discussing the question, though not with the detail of the book. Most are either paywalled or in PDF formats (which seems to strongly discourage online readers). Their quality and expertise strongly reward expended effort, do please read these if you're genuinely interested in the question.
https://lab.rockefeller.edu/cohenje/assets/file/257bCohenHow...
http://www.oneonta.edu/faculty/allenth/Class-Readings-Passwo...
A review of Cohen's book, "On Human Carrying Capacity: A Review Essay on Joel Cohen's: How Many People Can the Earth Support?"
https://www.jstor.org/stable/2137692 (http://libgen.rs/scimag/10.2307%2F2137692)
And a hearty recommendation from science fiction author Kim Stanley Robinson:
https://www.theguardian.com/books/2020/oct/12/there-is-no-pl...