As far as I know, Boltzmann brains became an issue in contemporary cosmology after a 2002 paper by Susskind, Kleban, and Dyson, “Disturbing Implications of a Cosmological Constant”. in which they specifically focus on Boltzmann brains in eternal De Sitter space, which is what you get if you assume that dark energy is constant and perpetual.
One thing that has changed since those days, is that the very existence of eternal De Sitter space in string theory or quantum gravity is in doubt, thanks to the “swampland” program which tries to identify worlds that aren’t possible. It’s controversial because the conception of the string “landscape” of possible worlds, that many people including Susskind promulgated in the 2000s, is heavily populated with De Sitter vacua. However, these were made using supergravity approximations and destabilizing mechanisms from full string theory have since been discovered.
So it may be that at the level of physical theory, the Boltzmann brain may disappear as an issue when counting cosmological observers, because De Sitter space simply doesn’t last long enough before decaying into flat space. Whether it is still an issue at Tegmark level 4, I couldn’t say, the structure of possibility there is too unclear to me.
There is also some debate over whether eternal de Sitter space would even exhibit the right kind of fluctuations to support Boltzmann Brains at all. See Boddy, Carroll & Pollack (2014) for a standard argument.
As far as I know, Boltzmann brains became an issue in contemporary cosmology after a 2002 paper by Susskind, Kleban, and Dyson, “Disturbing Implications of a Cosmological Constant”. in which they specifically focus on Boltzmann brains in eternal De Sitter space, which is what you get if you assume that dark energy is constant and perpetual.
One thing that has changed since those days, is that the very existence of eternal De Sitter space in string theory or quantum gravity is in doubt, thanks to the “swampland” program which tries to identify worlds that aren’t possible. It’s controversial because the conception of the string “landscape” of possible worlds, that many people including Susskind promulgated in the 2000s, is heavily populated with De Sitter vacua. However, these were made using supergravity approximations and destabilizing mechanisms from full string theory have since been discovered.
So it may be that at the level of physical theory, the Boltzmann brain may disappear as an issue when counting cosmological observers, because De Sitter space simply doesn’t last long enough before decaying into flat space. Whether it is still an issue at Tegmark level 4, I couldn’t say, the structure of possibility there is too unclear to me.
There is also some debate over whether eternal de Sitter space would even exhibit the right kind of fluctuations to support Boltzmann Brains at all. See Boddy, Carroll & Pollack (2014) for a standard argument.