Abstract
We show that in a large volume scenario of type IIB string or F-theory compactifications, single thermal inflation provides only a partial solution to the cosmological problem of the light volume modulus. We then clarify the conditions for double thermal inflation, being a simple extension of the usual single thermal inflation scenario, to solve the cosmological moduli problem in the case of relatively light moduli masses. Using a specific example, we demonstrate that double thermal inflation can be realized in large volume scenario in a natural manner, and the problem of the light volume modulus can be solved for the whole relevant mass range. We also find that right amount of baryon asymmetry and dark matter can be obtained via a late-time Affleck-Dine mechanism and the decays of the visible sector NLSP to flatino LSP.