Can the "Boltzmann brain" concept inform discussions of cosmology? The Boltzmann brain was originally discussed as a sort of thought-experiment or aid
to reflection on what might possibly happen in the universe. Its first discussion was
in the context of thermal equilibrium. The idea is that there is a non-zero chance that,
given enough time, a system such as a gas in thermal equilibrium and with the right
constituents might, by very rare random thermal fluctuation, come together in a remarkable
configuration such as a brain (with, I suppose, associated oxygen supply, heat removal, etc.)
This notion, sort of wierd and yet sciencey, captures the imagination and hence entered
the popular imagination about what physics says or might say. It enables one to pose a question such as,
"how can you tell whether you yourself, with all your memories and present experiences,
may not be such an entity? All your 'understanding' of cosmic and biological evolution might
be just a set of ideas created ready-made in your brain, the whole thing just the result of
thermal fluctuation in a gas?"
My question is, has this idea ever approached even approximately to a concept in which
people understand what they are talking about sufficiently well that it can support a
conclusion that could be falsified or otherwise connect with scientific discussion more
generally? It seems to me that attempts to calculate the probability of a Boltzmann brain
are simply back-of-the-envelope estimates that are almost certainly wildly off, and as
such have practically zero usefulness. A very tiny number $\nu$ which no-one knows how to
calculate, even approximately, is combined with a very large number $N$ (some notion of
an enormously long future for the universe, for example, or a vast number of different
universes) which is also something
we know little about, and then their product $N \nu$ is discussed. This $N \nu$
number appears to have some scientific credibility because it is invoked by reputable
scientists engaged in discussion about cosmological models and things like that.
I don't want this question to generate just a set of opinions. I am asking whether
there is evidence, or some sort of sound basis on which to affirm, that
(1) we understand the relevant probability distributions
sufficiently well to trust calculations of this sort (this would require, for example,
that one is treating the low-probability wings of the distribution correctly, and
accounting for correlated effects correctly)
(2) we know what is physically sufficient to give rise to the sorts of thoughts and experiences
enjoyed by humans (e.g. is a brain enough, or does one need a community and the exchange
of language, and a stimulating environment, etc.)
It seems to me that the correct answer to both these questions is a simple "no", but
if I am mistaken then I would be interested to know it.
 A: I think the Boltzmann brain argument is similar to the cosmological constant problem: it's an apparent prediction of current models that is clearly unacceptable, but it's not clear how to evade it. There obviously is something wrong with the calculation, but that's no reason to dismiss it out of hand without knowing how it's wrong.
The image of a lone brain floating in a vacuum is unfortunate. You may as well take the fluctuation to include, as you put it, "a community and the exchange of language, and a stimulating environment, etc." and whatever else is required, even astronomers and light en route to their telescopes that appears to show a ΛCDM cosmos. Given the absurd tininess of the probabilities that are involved anyway, this scarcely makes any difference. Many models have an infinite amount of vacuum so there's plenty of room for whatever nonsense you want to imagine in your random world. The problem isn't consistency or inconsistency with what we observe, it's that our whole model of how things came to be (cosmological+biological evolution) is seemingly just a tiny correction to a probability distribution dominated by tornado-in-a-junkyard processes.
The argument doesn't really depend on the absolute probability of any fluctuation, but on the idea that a fluctuation that would create an entire ΛCDM cosmos should be less common  than a fluctuation that just creates part of one. I don't really see why that should be true – there is a thermodynamic argument for it, but it seems weak – but that's just an opinion.
A: An endless, fluctuation dominated universe, like ours will be according to theory, will produce anything and everything allowable by the laws of physics an infinite amount of times. That is just the logical conclusion based on the assumptions of heat death and expansion.
That we are the type of observers we are (posses memories of the past, memories of a low entropy past, observe the second law, etc), Sean Carroll then uses statistics and Bayesian priors alone to a priori rule out BB's and their relevant cosmologies. So the mainstream cosmological theory must be wrong for Sean in this regard:

"The best we can do is to decline to entertain the possibility that the universe is described by a cognitively unstable theory, by setting our prior for such a possibility to zero (or at least very close to it). That is what priors are all about: setting credences for models on the basis of how simple and reasonable they seem to be before we have collected any relevant data."

Why are BB's (with our memories and experiences) cognitively unstable, and thus appropriate to rule out philosophically?

"On the one hand, we use our reasoning skills and knowledge of physics to deduce that in such a cosmos we are probably randomly-fluctuated observers, even after conditioning on our local data. On the other hand, we can also deduce that we then have no reason to trust those reasoning skills or that knowledge of physics. The randomly-fluctuating universe scenario is therefore self-undermining, or as Albert has characterized similar situations in statistical mechanics,cognitively unstable"

Others like Susskind say an infinite amount of BB's is not a problem if an infinite amount of observers like us also exist. With the proper measure we can recreate our experience of not observing BB's. What does Susskind posit as the method of generating infinite observers like us. A certain kind of multiverse. (paraphrasing his argument from https://youtu.be/jhnKBKZvb_U?t=2524) So Susskind has a way to preserve our current cosmological models unlike Carroll, at the expense of adding a multiverse. Our universe is still going to produce BB's in the far future, but there are enough observers like us in the total multiverse so that observers like us never witness BB's and by and large observe what we do (have memories, witness a second law, etc.)
No one can give the proper probability weights that you ask about in (1), partly because we don't know (2) precisely, and we also don't know how to handle the measure problem - if the universe really is infinite. But given that, Carroll and Susskind found ways to argue either side of BB's being real, without needing exact distributions. So I'm not sure (1) or (2) are necessary or sufficient to weigh in BB's in so far as they are unknown and yet prominent physicists are still talking about BB's.
A: As the formation of a "Boltzmann Brain" seems vastly more likely than the formation of the universe (or even the local universe) that that brain could be imagining, would an eventually exact recurrence of it not seem likely to occur on a much shorter time scale than the full-scale recurrence of the universe or multiverse that it would be visualizing?
Of course, the designation of it as a "B.B." simply provides, as any reader of Orwell's science-fiction novel "1984" should realize, an entertainingly repetitive sound in the style of poetry, ballads, chants, and jokes:  The content of the aforementioned fact about the (mathematically overwhelming) probability of recurrences (in any universe or multiverse that is, if not infinite and eternal, at least "extremely large"), has been stated as a caricature of a fact that does threaten conventionality in physics, although the conventionality that it actually threatens is simply the anthropocentric notion that our own spatial and temporal scale might reasonably be central amid the infinite and eternal possibilities that plainly may exist.
That notion could be corrected by use of the term "Boltzmann Minds", which might even be acceptable to Sean Carroll, who has suggested that cosmological models which do not prevent the formation of "Boltzmann Brains" should not be well-received.  (The duration of a biological "brain", in the cold reaches of intergalactic space, would--at least to us--seem infinitesimally brief:  How it would expand into smithereens, while at the same time remaining frozen more solidly than the cold heart of a glacier, might keep other experts debating for quite a large number of decades!)
In physics (whose successful use requires observational or experimental verification of its conclusions), the problem with any brain, as compared to that inanimate reality whose analysis might be misconstrued as a brain's main concern, is that a brain can, as well, produce counterfactual models (or, at least, models whose existence is not susceptible to the aforementioned verification).  Since the time of Giordano Bruno (burnt at the stake in 1600 Rome), the physical eradication of such disparities has been attempted, but, because it cannot be accomplished with that rapidity with which the universe appears to dispose of Boltzmann brains, such eradication has not (yet) proven to be practical.
Regarding "Boltzmann minds", there may have been only one so far, but its effects have been relatively enduring.  Among cosmological models, a favorite of my own has been Nikodem Poplawski's "cosmology with torsion"(described in 2010-2021 papers whose preprints remain freely visible on Arxiv), which seems to yield sequential reductions in spatio-temporal scale perhaps even more rapid (in some localities) than the quasi-instantanous disappearance of whatever Boltzmann brains might otherwise splatter across the windshields of our rocket ships.
However, Poplawski's cosmology does require a "preferred direction" of motion, resulting from the "inheritance" of the direction of rotation of the stars whose gravitational collapse initiates the genesis of its local universes by those localities themselves.  Conclusive evidence for such a prevalent direction has yet to be found, thereby leaving his model (at least for now) without the clear observational or experimental support required by science.
Nevertheless, a model that's similar (inasmuch as it does not require any magical or unmotivated "beginning" for reality) is provided by Penrose's "cyclic conformal cosmology", which postulates a gravitational entropy having effects inverse to those of the thermodynamic entropy involving the other fundamental forces, and, as I've mentioned in my comments on other answers formulated during this stimulating discussion, implies intermittent "endings of time" (for lack of the massive components required in every known or imaginable form of "clock") upon the gravitational decoherence of all particulate matter into radiation, and thereby allows the thermal equilibrium of each "aeon" to serve as the "big bang of the next", in what may be the most plausible scenario for purely spatial expansion:  There has been consistent evidence for the Penrose model in the observation of "Hawking points" (anomalous spots of significantly raised temperature in the CMB sky that result from the release of Hawking radiation by the "evaporation" of black holes), as discussed in the March 2020 paper at https://arxiv.org/abs/1808.01740.
A: I have heard about 'Boltzmann Brains'.
I generally took them to be yet more wild speculations based upon the supposition that the wilder the suggestion the more likely it is true. This is just wrong.
It captures the imagination of the public at large because of it's outlandishness. And it is of a piece with the current crisis over misinformation, disinformation, science denialism and fake news.
The way to think about life in cosmology is to understand it with how cosmology is understood. For example, the recent Kepler survey suggests that there is roughly forty billion earth like planets in the Milky Way, 11 billion of which orbit sun like stars.
Of these, we have currently established the existance of around 4,000 exoplanets.
This is well established science that gets closer to question of life outside of earth and hence establishing the existence of 'brains' in cosmology. If they exist - which I believe they do -they will exist in life like creatures on exoplanets.
A: The question is: Is the Boltzmann brain scientific? It might be sciency, but it is certainly not scientific. To believe that such a brain (or whatever structure, inclusive the entire universe that is visible now) can possibly come into existence is to deny the structures that can give rise to the non-Boltzmann brains.
Why is that? Actual brains somehow must develop in a universe fit for life This is why they have developed in a relatively short time when compared to a Boltzmann brain (the emergence of the Boltzmann brain itself for which a smile is meaningless because of the lack of directing structures itself though is instantly but it takes some time for it to emerge, to say the least). It's the only way a brain can,  form. So to acknowledge that a Boltzmann brain (by which I mean all structures, like the brain inside bodies, the Solar system, galaxies, etc.) exists is to acknowledge that the real brains don't exist. Who says we are not a floating brain in a post-life universe? Or, as you write:

"How can you tell whether you yourself, with all your memories and present experiences, may not be such an entity? All your 'understanding' of cosmic and biological evolution might be just a set of ideas created ready-made in your brain, the whole thing just the result of thermal fluctuation in a gas?"

Exactly. The idea undermines the reality of our whole existence. Though I doubt that you can have long time experiences in a Boltzmann brain, as it exists only for a short while. And why should its existence be short when all of the universe's content can be formed, and, once formed, why should it fall apart again? How should I type this answer with a Boltzmann brain?
It's just not possible that a Boltzmann brain forms in the way described. I.e., by the accidental coming together of a huge number of particles in the vast space of a universe after the warmth death has set in. I.e., in the thermodynamic equilibrium occurring in our universe after a long time.
Why should this be impossible? You can just as well ask, how should this be possible? It's easy enough to imagine that one day far away such a brain can come into existence. But can it come into existence like this? It comes into existence by chance without the mechanisms that are involved in the developments of real brains, humans, and their environments. I think something deep is missed when one thinks that a Boltzmann brain can come into existence. This something deep is just the existence of mechanisms that lead to the non-probabilistic formation of life and cosmos.
I don't see how a Boltzmann brain can inform discussions about cosmology though. Which is what you ask. Maybe you can say that if your cosmology involves a universe (cosmos) that is limitless in time (and without a big-bang-big-crunch sequence) and you believe in the existence of Boltzmann brains then you will never be sure if you live in the real world or in the Boltzmann world. And maybe the existence of a Boltzmann brain should have to make you doubt the second law (of thermodynamics) itself. How can a universe which looks the same as the universe today come into existence? Why should such a universe exist only be for a short while? If so, then it's certainly not the same as the present universe .
