The fate of Poincaré recurrence with the Big Rip Recently, there has been a lot of talk in the media about the "Big Rip". It most certainly resulted from the paper by Marcelo M. Disconzi and Thomas W. Kephart where they have figured out a mathematical system that allows the state parameter of the vacuum energy to drop below -1. Obviously this means the big rip is a possibility (perhaps a certainty?) and they have calculated the time frame to be 22 billion years. My question is what happens to the Poincaré recurrence theorem in a big rip universe? Is it still a possibility? And if yes then does the big rip lead us back to the classic Boltzmann brain situation? 
 A: Regarding the commentary posted by the OP and by Curious One, wouldn't observational data include any decrease in that proportion of space where every line of sight ends at a star? We've seen evidence for that decrease, in more than 90 formerly binary stars whose onetime partner has disappeared, through the fact that each of the surviving partners still follows the elliptical orbit it once shared with that partner.
Another part of the process (that acceleration of spatial expansion which was first discovered by each of two rival teams of researchers in the late 1990's) would plainly be consistent with the start of a Big Rip.  The disintegration that precedes recurrence is a necessary prelude to the recurrence itself, and the processes involved may have evidently begun, even within our observable region.
The cosmological model most consistent with these processes may be the "Cosmology with torsion" formulated, since 2010, by Nikodem Poplawski, using 1929's Einstein-Cartan Theory rather than 1915's General Relativity:  In ECT, a tiny spatial extent (some orders of magnitude greater than the Planck length) was assigned to fermions, previously considered to be point-like.  ECT was formulated by Einstein in collaboration with the mathematician Cartan,  after the discovery (in the mid-1920's) of particulate spin.   Poplawski's model provides a version of cosmic inflation, but does not require a field of  "inflaton" particles, that do remain entirely hypothetical.
In the torsion-based model, any large rotating star that's collapsing under its own weight (after expenditure of its nuclear fuel has left it with radiation pressure insufficient to prevent its collapse) begins the formation of a black hole:  In a single bounce or a series of smaller bounces, fermions newly-materialized by separation from  their partners in virtual pairs, through tidal effects in the intense gravitational field within the collapsing stellar volume, are spun outward through contact with the stellar fermions (initially much larger) within that volume, to form a new "local universe" that's causally separated (like all black holes) from the larger multiverse within which all of this activity is occurring.  The shape of each such new LU has been analogized by Poplawski to "the skin of a basketball", and clearly fits the description of a closed (but local) universe, within a larger inflationary multiverse.
The causal separation is essential for  Poincaré recurrence, formulated by  Poincaré in 1890 and proven mathematically correct by Cathéodory in 1919, which provides for nearly-identical arrangements of particles to appear, at extremely long intervals of time, within any closed  volume.  That separation consequently provides the simplest explanation for the fact that, although the multiverse may be isotropic, as well as incomparably larger than our observable region, every line of sight from the earth does not end at a star.  As each local universe in Poplawski's model inherits its "arrow of time" from its parent, the model has the "falsifiable" nature required of scientific theories, and there has been some data (by Cai and by Lior Shamir), showing a prevalent direction of motion, which tends to support it:  However, given the size (for us) of our Observable Region, and the strong possibility that there are many sequences of black holes on sequentially- decreasing spatio-temporal scales, definitive proof may remain unlikely for a while.
Although Poplawski's model was found to be consistent with the CMB data in a preprint by Desai titled "Non-parametric reconstruction of an inflaton potential" that (like preprints of the many papers, written by Poplawski between 2010 and 2021, detailing his model) can be seen freely on Cornell University's Arxiv website, it remains unpopular in some parts of the world, perhaps partly because of ECT's exceptionally complex notation, but also because his cosmological model is one of several that are potentially eternal to the past as well as to the future, and are, consequently, unpopular with creationistic religions that remain politically and economically influential in some state and private university systems within the United States, as well as in some other regions.
The paper by Visconzi et al that the OP has cited (titled "A new approach to cosmological bulk viscosity"), posits (within its first few paragraphs) a future singularity, but Poplawski's past- and future-eternal model "avoids" (to use the terminology employed by its author) any singularity. At least by my reading of the verbiage in Poplawski's 2010 model, in conjunction with some resemblances of it to Roger Penrose's "Conformal cyclic cosmology" (also formulated in 2010, & also past- and future-eternal, but differing from it in a dependence on singularities), the difference between ECT and GR may explain this.  (Poplawski's 2010 paper was subtitled "An alternative to cosmic inflation", but has generally been considered to present a variant of inflation, which can most simply be described as asymptotically-exponential spatial expansion.)
