Is Carroll-Chen's AS-dS time-reversing inflationary model true?

• Clarifying the question (Describing the model)

  In 2004, Sean Carroll and Jennifer Chen published this model in a paper titled “Spontaneous Inflation and the Origin of the Arrow of Time.”¹ The model has several parts and can perhaps best be explored as a series of chronologically successive stages.
  STAGE 1: Mother Universe contracts inward from eternity past.
  STAGE 2: Mother Universe bounces at a minimal size.
  STAGE 3: Mother Universe expands; eventually her content (matter, black holes etc.) entropically dissolves into a low-heat energy blanket.
  STAGE 4: The energy-blanket is soil for chance fluctuations to produce baby universes, like ours. See elaboration on these stages below.

  1. “Spontaneous Inflation and the Origin of the Arrow of Time,” [arXiv:hep-th/0410270] (2004). They subsequently proffered an alternative modified version through 2006-2010.

• Exploring the stages in Carroll-Chen's model

  STAGE 1: From eternity past there has existed a mother universe which never began to exist. During its entire existence so far, it has been contracting to a smaller and smaller size. Interestingly, temporal events have all been playing in reverse during this contraction phase. After all, the “order” in which things naturally evolve from nebula to galaxies, galaxies to solar systems etc. is considered a function of entropy (the 2nd Law of Thermodynamics). This “thermodynamic time” however, is reversed during the contraction phase; so an observer progressing through real time during this phase would see everything play backwards: corpses come to life, milk stirs out of coffee, eggs unscramble back into their shell, and so forth.
  STAGE 2: At some point, the contracting mother universe reached a particular microscopic size (though not a singularity). This minimal size constituted a “bounce” point. Up until this point, entropy has been decreasing with contracting space. Now, at this bounce point, entropy (thermodynamic time) is the least evolved that it has ever—and will ever—be.
  STAGE 3: From the bounce phase, Universe then underwent mirror-like expansion phase which entropically decays into an empty space over time. (It asymptotes into a De Sitter phase; so it is called “Asymptotically DeSitter.”)

  Sean Carroll & Jennifer Chen: “As our universe expands… structures are still forming and complex life forms are riding the wave of entropy generated by hot suns shining in cold skies. But ultimately those stars will grow dim, galaxies will collapse into black holes, black holes will evaporate, and all we will be left with is an increasingly thin gruel of elementary particles in a background of vacuum energy. That, then, is a high-entropy state: a nearly-empty universe suffused with a tiny amount of vacuum energy." This space “…is empty apart from the thin background of thermal radiation…” ([2006], p. 1134; [2010], p. 355; [2010], pp. 362-3). [That it to say, it’s an expanding space with only dilute unusable energy blanketed throughout.]

  STAGE 4: Carroll-Chen mention this De Sitter space can entropically evolve via the entropy produced in baby universes that it spawns. They say it may spawn baby universes a few different ways:
  (A) Eternal Inflation: An inflation field fluctuation spontaneously kicks-off “eternal inflation.”
  (B) Vilenkin Tunneling: Quantum tunneling occurs “from nothing.”
  (C) Old Inflation: Quantum tunneling occurs “from a small patch of false vacuum.”
  They express reservations about Old Inflation, and opt primarily for slow-roll Eternal Inflation inflation. See “Inflation Field” [Forthcoming] for necessary background concepts.

  Sean Carroll & Jennifer Chen: “Given the nonzero Gibbons-Hawking temperature, there will necessarily be fluctuations in the scalar field… There is therefore some chance that the field can spontaneously fluctuate all the way up to φe in a patch of radius H−1e , thereby providing an appropriate initial condition for the onset of inflation.” [“Spontaneous Inflation and the Origin of the Arrow of Time,” [arXiv:hep-th/0410270] (2004), 23.]

  Of this kind of fluctuation, they admit, “The probability is of course small, but if we have infinitely long to wait it will eventually occur.” [Ibid.] One of these baby universes, it is suggested, is our universe. Interestingly, since the expansion phase mirrors the contraction phase in storage 1, there is a .5 likelihood that in fact we are in the contracting phase and unwittingly marching through time in thermodynamic reverse!

  1. Sean Carroll & Jennifer Chen: “Eventually, thermal fluctuations in this background allow a scalar inflaton field to bounce sufficiently high up its potential that eternal inflation begins with a large vacuum energy. Different parts of this inflating region fall down the potential, reheating and evolving into galaxies as in the conventional picture; elsewhere, inflation continues forever. [“Spontaneous Inflation and the Origin of the Arrow of Time,” [arXiv:hep-th/0410270] (2004), 27.]

• It implies you're a Matrix brain that just popped into existence

  The model implies you are probably a brain that just popped into empty space with Matrix-like beliefs (E.g. falsely thinking you have a body, previous birthdays, and that you're really right now reading something that exists external to your mind.) After all, far more of these kinds of brains are created in the Carroll-Chen model than real brains that have evolved over time. (Specifically, the model runs into Poincare recurrence version of the Boltzmann Brain scenario)¹

  1. After all, for each baby universe formed, there is exactly one actual Big Bang expansion, but the potential for innumerably many Boltzmann Brain’s with spontaneously created beliefs about being in a Big Bang universe. The baby universe may yield baby universe’s of its own, but for each and every baby universe the same ratio applies: one actual internal Big Bang expansion phase vs. innumerably many Boltzmann Brains over time. A philosophy of physics specialist introduced this problem.

     Eric Winsberg (Philosophy professor at USF): “it is far from clear that the most plausible thing to think is that, even in a branching multiverse, BB with big-bangy memories and records will not still vastly outnumber real big bangs—even though there are now a whole lot more big bangs than there were in the single Universe (only one!). That’s because it seems plausible to suppose that as each new Universe springs into being, it creates exactly one new actually big-bangy state, but the potential for innumerably many BBs with big-bangy memories and records. And so even on the multiverse model, it still seems plausible to suppose that, from only the evidence that is at my disposal and from the postulates of the model, it is still overwhelmingly more likely that I am a BB than that I have veridical records of a big-bangy past.” [“Bumps on the Road to Here (from Eternity)”, Entropy 14 (2012), 404.]

• It requires a highly improbable bounce stage.

  The model requires a highly improbable bounce stage. After all, it allegedly avoids singularities, but in order to avoid such singularities it has to be highly fine-tuned (not "generic" at all as proposed).¹

  1. Alexander Vilenkin: “[the scenario] proposed by Carroll and Chen,.... does require special boundary conditions at the bounce. ...[otherwise the hourglass inflating regions] will be surrounded by singularities and will have singularities in their past or future.” [“Arrows of time and the beginning of the universe,” Phys. Rev. D 88 (2013) 043516.]

• The model destroys probability

  The model “wreaks havoc on probability judgments”.¹ This is relevant because human probability judgments are justified (e.g. we are justified in believing that dinosaur bones are actually evidence of dinosaurs having existed, that everyday objects obey gravity predictions, that Rome actually existed etc.). This so-called “measure problem” seems intractable for many multiverse models, and certainly plagues the Carroll-Chen model.²

  Paul Steinhardt: “Many remain hopeful even though they have been wrestling with this issue for the past 25 years and have yet to come up with a plausible solution.” [“The Inflation Debate: Is the Theory at the Heart of Modern Cosmology Deeply Flawed?”, Scientific American (April 2011), 42.]

  1. If everything is happening an infinite number of times, then what is you’re dealing with ratios of infinity:infinity.

     Christopher Weaver: “[t]his wreaks havoc on probability judgments. If your sample space is infinite, it does not appear possible to have a well-defined probability measure to underwrite your probability and likelihood judgments. This problem of infinities and probabilities in eternal inflation-based cosmologies is well-known. However, it is also well-known that there is no current satisfactory solution to the problem.”

  2. Alan Guth: “…we still do not have a compelling argument from first principles that determines how probabilities should be calculated.” (2004), 50.]
     Steinhardt and Turok: “What is the probability distribution? In models such as eternal inflation, the relative likelihood of our being in one region or another is ill-defined since there is no unique time slicing and, therefore, no unique way of assessing the number of regions or their volumes. Brave souls have begun to head down this path, but it seems likely to us to drag a beautiful science towards the darkest depths of metaphysics.” [(2005), 44.]