While the simplest models of inflation provide an appealing simple framework giving excellent agreement with observations, it is important to consider whether a similar outcome might arise from a more complicated set-up that has better motivation from fundamental physics. There are some new ideas circulating in this regard, of which I will highlight just two related ones.
6.1. The braneworld
Particle physicists generally tend to believe that our Universe really possesses more than three spatial dimensions. Previously it has been assumed that the extra ones were "curled up" to be unobservably small. A new idea is the braneworld, which proposes that at least one of these extra dimensions might be relatively large, with us constrained to live on a three-dimensional brane running through the higher-dimensional space. Gravity is able to propagate in the full higher-dimensional space, which is known as the bulk.
This radical idea has many implication for cosmology, both in the present and early Universe, and so far we have only scratched the surface of possible new phenomena. Already many exciting results have been obtained - see the article by Wands in these proceedings. I'll just consider a few pertinent questions.
1. Are there modifications to the evolution of the homogeneous
The answer appears to be yes; for example in a simple scenario (known as Randall-Sundrum Type II ) the Friedmann equation is modified at high energies so that, after some simplifying assumptions, it reads 
where is the tension of the brane. This recovers the usual cosmology at low energies << , but otherwise we have new behaviour. This opens new opportunities for model building, see for example Ref. .
2. Are inflationary perturbations different?
Again the answer is yes - there are modifications to the formulae giving scalar and tensor perturbations . Unfortunately the main effect of this is to introduce new degeneracies in interpretting observations, as a potential can always be found matching observations for any value of . The initial perturbations therefore cannot be used to test the braneworld scenario.
3. Do perturbations evolve differently after they are laid down on
The answer here is less clear. It is certainly possible that perturbation evolution is modified even at late times. For example perturbations in the bulk could influence the brane in a way that couldn't be predicted from brane variables alone. Whether there is a significant effect is unclear and is likely to be model dependent.
6.2. The Ekpyrotic Universe
It has recently been proposed that the Big Bang is actually the result of the collision of two branes, dubbed the Ekpyrotic Universe ; this scenario is discussed in detail in Turok's article in these proceedings. It has been claimed that this scenario can provide a resolution to the horizon and flatness problems, essentially because causality arises from the higher-dimensional theory and allows a simultaneous Big Bang everywhere on our brane, though existing implementations solve the problem by hand in the initial conditions. As I write this, it remains unclear how to successfully describe the instant of collision between the two branes (the singularity problem), and considerable controversy surrounds whether or not the scenario can also generate nearly scale-invariant adiabatic perturbations . Both aspects are required to make it a serious rival to inflation.