During the past-infinite contracting phase, the whole space becomes thermalized1 This is relevant because if a space is entirely thermalized, it is no longer de Sitter; instead of a bounce and expansion, the thermalized space ends in a big crunch.2
The model requires “acausal fine-tuning.” (That is to say, the entropic evolution is extraordinarily fine-tuned1, and yet logically eliminates any hope of explaining it.) This is relevant because it means the so-called prior probability of the model being true is irresolvably something like 1 over infinity; i.e. the chances of it being true prior to examining the evidence for and against it are virtually zero, and so the model would correspondingly require almost incomprehensively good evidence to overcome its implausibility.
• Alexander Vilenkin: “The Aguirre-Gratton model can avoid singularities by postulating a small “initial” closed universe and then allowing it to evolve in both directions of time. I put "initial" in quotation marks, because Aguirre and Gratton do not think of it that way. But this model requires that a very special condition is enforced at some moment in the history of the universe. At that moment, the universe should be very small and have very low entropy. Aguirre and Gratton do not specify a physical mechanism that could enforce such a condition.” [E-mail to William Lane Craig: reasonablefaith.org/honesty-transparency-full-disclosure-and-bgv-theorem]
• Andreas Albrecht: “In the Aguirre-Gratton construction, the arrow of time is put in by hand. One simply declares 'the universe is in this state,' and it happens to have an arrow of time. [389.] ... “The eternally inflation state that emerges from that approach has specific global properties that reflect an arrow of time. In particular, an array of regions of reheating (or decay of the potential-dominated state) must be organized coherently to be pointing in a commonly agreed ‘forward direction.’ In fact, there are actually two different ‘back-to-back’ coherent domains in this picture, with arrows of time pointing in opposite directions. The coherence must extend over infinitely many reheated regions, distributed throughout an infinitely large spacetime volume.” [Science and Ultimate Reaity (Cambridge, 2004), 388.]
• Sean Carroll: “Why is the entropy so low in the middle of the history of the universe? In other words, the bouncing-entropy model doesn’t, by itself, explain anything at all about the arrow of time. Rather, it takes the need for a Past Hypothesis and replaced it with the need for a “Middle Hypothesis.” There is just as much fine-tuning as ever; we are still stuck trying to explain why the configuration of our coming patch of space found itself in such a low-entropy state near the cosmological bounce.” [From Eternity to Here (), none-given.]
The Aguirre-Gratton model undercuts causal reasoning (in life and science) (After all, the model yields two mirror halves, so there's a 50% chance we are the half experiencing time in thermodynamic reverse.) This is relevant because its an absurd conclusion and even undercuts justification for belief in the model itself.1