There are a number of interesting open questions connected with inflation:

**The origin of the Inflaton:** It is far from clear what the inflaton
actually is and where its potential comes from. This is intimately
connected with the question of why the perturbations have the amplitude
and spectrum they do. Currently, there is much confusion about
physics at the relevant energy scales, and thus there is much
speculation about different possible classes of inflaton potentials.
One can hope that a clearer picture will eventually appear as some
deeper theory (such as string/M theory) emerges to dictate the
fundamental laws of physics at the inflation scale.

**Physics of the inflaton:** Having chosen an inflaton
potential, one can calculate the
perturbations produced during inflation *assuming* the relevant
field modes for wavelengths much smaller than the Hubble radius are in
their ground states. This seems plausible, but it
would be nice to understand this issue more clearly. Also, the
inflaton field often takes on values *O*(*M*_{P}). Will a
yet-to-be-determined theory of quantum gravity introduce large
corrections to our current calculations?

**The cosmological constant problem:** A very important open question is
linked with the cosmological constant
problem [26,
27,
28].
The non-zero potential energy of the
inflaton during inflation is very similar to a cosmological constant.
Why the cosmological constant is extremely close to zero today (at
least from a particle physicist's point of view) is perhaps the
deepest problem in theoretical physics. One is left wondering whether
a resolution of this problem could make the cosmological constant and
similar contributions to Einstein's equations identically zero, thus
preventing inflation from every occurring. Interestingly, current data
is suggesting that there is a non-zero cosmological constant today
(see for example Fig. 11 which shows
_{} = 0 is
strongly excluded). Cosmic acceleration today is a very confusing
idea to a theorist, but it actually is helpful to inflation theory in
a number of ways: Firstly it shows that the laws of physics do allow
a non-zero cosmological constant (or something that behaves in a
similar way). Also, it is only thanks to the non-zero
_{} that the current data are
consistent with a flat Universe (see
Fig. 11).

**Wider context and measures:** We
discussed in Section 3.4 various ideas about how an
inflating region might emerge from a chaotic start. This is a very
challenging concept to formulate in concrete terms, and not a lot of
progress has been made so far. In addition, the fact that so many
models are ``eternally inflating'' makes it challenging to define a
unique measure for the tiny fraction of the universe where
inflation actually ends. It has even been
argued [29,
30,
31] that these
measure problems lead to ambiguities in the ultimate predictions from
inflation.

In fact it is quite possible that the ``chaotic'' picture will extend
to the actual inflaton as
well [32,
33].
Fundamental physics may provide
*many* different flat directions that could inflate and
subsequently reheat, leading to many different versions of the ``Big
Bang'' emerging from a chaotic start. One then would have to somehow
figure out how to extract concrete predictions out of this apparently
less focused space of possibilities.

I am actually pretty optimistic that in the long run these measure issues can be resolved [34]. When there are measure ambiguities it is usually time to look carefully at the actual physics questions being posed... that is, what information we are gathering about the universe and how we are gathering it. It is the observations we actually make that ultimately define a measure for our predictions. Still, we have a long way to go before such optimistic comments can be put to the test. Currently, it is not even very clear just what space we are tying to impose a measure on.

I am a strong opponent of the so-called ``anthropic'' arguments. All of
science is ultimately a process of addressing conditional probability
questions. One has the set of all observations and uses a subset of
these to determine one's theory and fix its parameters. Then one can
check if the theoretical predictions match the rest of the
observations. No one really expects we can predict all observations,
without ``using up'' some of them to determine the theory, but the
goal of science is use up as few as possible, thus making as many
predictions as possible. I believe that this goal must be the only
determining factor in deciding *which* observations to sacrifice
to determine the theory, and which to try and predict. Perhaps the
existence of galaxies will be an effective observation to ``use up'' in
constraining our theories, perhaps it will be the temperature of the
CMB. All that matters in the end is that we predict as much as possible.

Thus far, using ``conditions for life to exist'' has proven an extremely vague and ineffective tool for pinning down cosmology. Some have argued that ``there must be at least one galaxy'' for life to exist [35, 36, 37], but no one really knows what it takes for life to exist, and certainly if I wanted to try and answer such a question I would not ask a cosmologist. Why even mention life, when one could just as well say ``we know at least one galaxy exists'' and see what else we can predict? In many cases (including [35, 36, 37]) the actual research can be re-interpreted that way, and my quibble is really only with the authors' choice of wording. It is these sorts of arguments (carefully phrased in terms of concrete observations) that could ultimately help us resolve the measure issues connected with inflation.