Tipler claimed that eternal growth was impossible in an expanding universe. >From page 139 of Physics of Immortality:
: As I discussed in Chapter III, Freeman Dyson pointed out that, although
: the energy is available in open and flat universes, the information
: processing must be carried out over larger and larger proper volumes.
: This fact ultimately makes impossible any communication between opposite
: sides of the 'living' region in a flat universe, because the redshift
: implies that arbitrarily large amounts of energy must be used to signal,
: and Dyson showed that only a finite amount of energy is availble.
: On the other hand, open universes expand so fast in the far future that
: it becomes impossible for structures to form of sufficiently larger and
: larger size to store a diverging amount of information.
He also claims that such dodges as ducking into basement universes wouldn't work; you can only put a limited amount of information into them.
There are a variety of new cosmological models which are being advanced to explain the recent measurements. The January issue of Scientific American has three articles describing different possibilities.
Tipler's analysis was apparently based on the classical open universe. Possibly it would not apply to non-contracting universes in the more complex models. Maybe the rate of expansion would be different enough that the communication problem he describes could be solved. I don't know.
If you really, really wanted to, you could invoke a cosmological constant which was repulsive in the past (explaining the observed expansion rate) but will become contractive in the future, so that the universe eventually contracts. There is no evidence for this, and no reason for the CC to change value, but it presumably can't be ruled out. Theories like two-part inflation have a somewhat similarly arbitrary quality, although in that case the complexity is introduced in order to explain observations.