In the similar spirit to Kallosh, Thomas grimm has a paper in arxiv on axion inflation in the context of type II string theory. The general outline is Grimm considers type IIB string theory on a compact CY with non trivial vanishing two cycles(example being a conifold). These two cycles are associated with axions whose fields depend on geometric moduli and also NS-NS and B-field.

 If string theory is the most fundamental theory, many feel that string theory should be part of the inflationary picture. Renata Kallosh has been working with stringy inflationary models and she and her collaborators have a new paper at arxiv titled “Axion Inflation and Gravity waves in string theory.” 

The paper outlines the problems of embedding string theoretic models to inflationary cosmology and they have found it difficult to to get rid volume moduli to obtain a flat axion.  So after no success in stringy models, they look at supergravity models with axion independent Kahler models where they show that inflationary graviatational wave (IGW) to be possible. An interesting thought that is suggested is the study of type IIB orientfold models which may give axion independent(quadratic shift symmmetric) Kahler models.

Here is the link:

Also one may be interested in Kallosh’s earlier paper (talk) which is much more general and describes the string theoretics inflationary models with flux compactification and moduli stablization.

Any comments(general or specific) are welcome.

Update: Incidentally Lubos Motl has a small comment on a paper by Bezrukov and Shapsoshnikov where they think about inflation from Higgs Boson. Their claim requires non-minimal coupling of the Higgs scalar field to gravity which leads to the amplitude of scalar perturbation to be proportional to square of Higgs Mass with coefficient terms.