Cosmological inflation [1, 2, 3] is widely perceived as an excellent paradigm within which one can explain both the global properties of the Universe and the irregularities which give rise to structures within it. Despite this, it remains fair to say that as yet the inflationary paradigm has been confronted with only a few observational challenges, which it has comfortably surmounted. In years to come, it will face many more, and the purpose of this article is to discuss which of these tests are likely to be the most stringent.
In doing so, it is worthwhile to separate out the two key roles that inflation plays in modern cosmology. The first, which led to its introduction, is in setting the `initial conditions' for the global Universe, by arranging a large homogeneous Universe devoid of unwanted relics such as monopoles. In terms of these global properties, it now seems unlikely that any new observations will undermine the inflationary picture, and, as Linde has argued , if it is to be supplanted that is likely to be because of the advent of a superior theory, rather than of superior observations. Accordingly, I will have little to say on this topic.
The second role, which is potentially much more fruitful as a probe of high-energy physics, is that inflation provides a theory for the origin of perturbations in the Universe (for reviews, see Refs. [2, 5]). As these perturbations are believed to evolve into all the observed structures in the present Universe, including the existence and clustering of galaxies and the anisotropies in the cosmic background radiation, this proposal is subject to a wide variety of observational tests. Thus far, these tests have been rather qualitative in nature, but in the near future inflation as a theory of the origin of structure in the Universe will face precision testing.
The challenge facing cosmologists is therefore to address two questions:
Unfortunately, in science one never gets to prove that a theory is correct, merely that it is the best available explanation. The way to convince the community that a theory is indeed the best explanation is if that theory can repeatedly pass new observational tests. In that regard, it is important to be as clear as possible concerning what these tests might be.