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We show that in a large volume scenario of type IIB string or F-theorycompactifications, single thermal inflation provides only a partial solution tothe cosmological problem of the light volume modulus. We then clarify theconditions for double thermal inflation, being a simple extension of the usualsingle thermal inflation scenario, to solve the cosmological moduli problem inthe case of relatively light moduli masses. Using a specific example, wedemonstrate that double thermal inflation can be realized in large volumescenario in a natural manner, and the problem of the light volume modulus canbe solved for the whole relevant mass range. We also find that right amount ofbaryon asymmetry and dark matter can be obtained via a late-time Affleck-Dinemechanism and the decays of the visible sector NLSP to flatino LSP.

Cosmological moduli problem in large volume scenario and thermal inflation