If Aguirre and Gratton's version of dual arrows of time in an inflationary reality (at http://arxiv.org/pdf/gr-qc/0301042v2.pdf) corresponds to our own, the past and future began their ongoing separation an infinite time ago, and, with its past spacetime contracting (as per Vilenkin's reading of AG, at http://arxiv.org/pdf/1305.3836v2.pdf), the most remote past is infinitely remote. It seems to me that, with the present spacetime presumably expanding into an infinitely remote future, the net curvature of the space between any objects having mass, in any one of two pairs of such objects each on an opposite side (past or future) of that reality from the other, would (if averaged between both pairs of them to yield amounts of mass) consequently add up to the zero characterizing a flat (Minkowski) vacuum, but the mass of either pair during its instant of passage through the present either would yield, or would've been yielding, the net positive figure characterizing de Sitter space. I'm thinking this could be either more or less plainly the case in the more generally accepted versions of inflation as "eternal to the future" (which Aguirre logically describes as "semi-eternal inflation"), depending on their account of the origin of the space-curving mass. I'm mainly wanting to verify whether my assumption of the "true" (meaning "minimum mass") vacuum as having mass is correct, because of a conclusion (based on the Many Worlds interpretation of QM and contained in the recent paper "De Sitter Space Without Dynamical Quantum Fluctuations", at http://arxiv.org/abs/1405.0298) that inflation would generically continue into the future only if the true vacuum is de Sitter. (In defense of the scientific method's popularity in its competition with other philosophies or ideologies equally engaged in various attempts at resolving our world's current social problems, I should mention the fact that the paper does allow for the universes described by an arbitrarily small number of branches of the wavefunction to inflate eternally, which has the interesting effect of explaining how any individual might involuntarily wander discontinuously between different settings, whereas generically eternal inflation would associate recurrences of every individual with a setting, identical to their oldest or original environment, that would tend to appear at random intervals.) However, it also occurs to me that a presumed dependence of the simultaneity of events perceived by different observers on their relative directions of motion (associated with Special Relativity by Brian Greene, on p.504 in The Fabric of the Cosmos) might not hold if gravity (absent in SR) could be taken into account. Consequently, a second question I have is whether a successful quantum theory of gravity would be expected to resolve such issues as the Train Paradox, which are routinely described in popularizations of SR and might, through the "block universe" view of time, allow an overlapping of realities that might give greater "weight" to either the past or the future, perhaps admitting Minkowski space to physicality, either at the origin of time or at its center. Any opinions on either of these two questions would be much appreciated.