An interesting implication of cosmic inflation from New Scientist which I found via Dave Pearce: "Time need not end in the multiverse." I think this passage most clearly explains the idea:

In a multiverse that grows exponentially, where each new generation of universes is far larger than the last, younger universes always outnumber older ones. Waking up, you will either be in a universe in which 1 minute has passed (heads), or in a universe in which 1 hour has passed (tails). "The experiment sets up a 59-minute ambiguity in the age of the universe," Guth says. "You should always bet on the younger one."

This raises the question of why we find our universe so old. Evolution took billions of years to produce us, but that process could have happened much faster. Moreover, other universes with different laws of physics will produce life-supporting conditions sooner after their big bangs. To the extent this holds, we have anthropic evidence against the theoretical apparatus within which cosmic inflation makes this prediction.

An alternate escape route is to suppose we're in a simulation of a universe that's older than it is. But the motives for simulators to put their creatures into statistically-unlikely-old universes seem dubious.

Perhaps the biggest problem with the scenario is that it relies on a hack of slicing time at any given instant to avoid infinity problems. Maybe there's a better way to conceptualize the measures here.

If the idea is correct, are there implications for action? I don't see any immediately, since, unlike the doomsday argument, this scenario doesn't talk about how long we'll continue to exist, just how long we should expect to have existed already.

The obvious answer is that we're not in such a multiverse.

Supposing we were in one, that would mean that any possible universe would have to exist eventually. Would two identical people in different universes count separately for the purposes of anthropic arguments? If not, that would that mean that you're equally likely to experience any combination of sensory input?

If we're in one, why are we in such an early one? I don't know which one it is, but whatever it is, you'd expect it to be later.

I avoid the concept of infinity because it tends to destroy expected value.

DanielLC wrote:Supposing we were in one, that would mean that any possible universe would have to exist eventually.

Any physically possible universe, yes, but not any universe is physically possible. One single universe likely has only a finite number of possible configurations at a given time. And even if the physical constants of different universes can take a continuum of values, this doesn't mean all possibilities are realized: cf., say, the sigmoid function, which takes an infinite number of inputs but only produces outputs in (-1, 1).

I think all physical possibilities do exist, but with different measures. You have to accept this if you buy many-world QM, so why not accept it for chaotic inflation too? You may have seen Max Tegmark's multiverse hierarchy.

DanielLC wrote:Would two identical people in different universes count separately for the purposes of anthropic arguments? If not, that would that mean that you're equally likely to experience any combination of sensory input?

Yes. No.

What exactly would it mean for the later universes to be more common? You could try taking the limit as the cutoff range increases or something like that, but there's no reason it has to converge.

Is there any specific reason to believe the universe behaves like this?

DanielLC wrote:You could try taking the limit as the cutoff range increases or something like that, but there's no reason it has to converge.

That's what the physicists in the article do. You're right it may not converge; the physicists just looked at fixed slices and hence got weird results.

A friend suggested that the paradox depends on how the limit is taken. If, instead of time slices, you pick number of completed universe-histories as your sequence, the time-truncation goes away.

DanielLC wrote:Is there any specific reason to believe the universe behaves like this?

General inflation has good evidence for it. I'm not sure how established these particular variants are, but I think a good fraction of cosmologists subscribe to them.

A friend suggested that the paradox depends on how the limit is taken. If, instead of time slices, you pick number of completed universe-histories as your sequence, the time-truncation goes away.

Their paradox isn't very big. The big one is that the answers change depending on how you take the limit.

General inflation has good evidence for it.

Can you be more precise? From what I understand, the space of the universe is expanding, but not the energy. Also, the universe is infinite (and always was) if the net curvature of spacetime is non-positive and matter is spread out evenly. I'm not sure why matter should be spread out evenly, but I've never seen anything suggesting it isn't.

DanielLC wrote:Their paradox isn't very big. The big one is that the answers change depending on how you take the limit.

Indeed. Actually, that's why the physicists adopted this method of looking at the distribution after only a finite time. From the article:

In any infinite multiverse, everything that can happen, will happen - an infinite number of times. That has created a major headache for cosmologists, who want to use probabilities to make predictions, such as the strength of the mysterious dark energy that is accelerating the expansion of our own universe. How can we say that anything is more or less probable than anything else?

One procedure physicists are fond of is to draw a cut-off at some finite time, count up the number of events - say, heads and tails - that occur in the multiverse before the cut-off time, and use that as a representative sample.

DanielLC wrote:From what I understand, the space of the universe is expanding, but not the energy. Also, the universe is infinite (and always was) if the net curvature of spacetime is non-positive and matter is spread out evenly. I'm not sure why matter should be spread out evenly, but I've never seen anything suggesting it isn't.

I don't profess to understand exactly, but I think chaotic inflation is different from whether our universe is open or closed. Chaotic inflation postulates a "sea of bubbles," each of which is its own big bang. We're one of infinitely many universes. Two popular books that I've read (which doesn't mean understood completely) were The Inflationary Universe by Alan Guth and Many Worlds in One by Alex Vilenkin.

See this paper's discussion of the "youngness paradox." http://arxiv.org/PS_cache/hep-th/pdf/0702/0702178v1.pdf

Great reference, Carl! Section 1 reviews some of the evidence for inflation. Section 4 explains DanielLC's point that averages taken over the universes can be sensitive to the order in which they appear in the sequence used for taking a limit. Section 5 explains the "youngness paradox."