Cosmological perturbations in multiple-field inflation
  We analyze cosmological perturbations to the linear order in the context of inflation with an arbitrary number of scalar fields. The fields take values on a non-trivial manifold with a positive-definite metric and are non-minimally coupled to Einstein gravity. The perturbations are decomposed into three different types. The scalar-type perturbations are presented in a gauge-ready form without fixing the temporal gauge condition, as well as in terms of gauge-invariant variables. The gauge-ready method enables us to impose different gauge conditions which are most suitable to the problem at hand. We quantize the scalar perturbations and obtain the solutions. 
Joydev Lahiri and Gautam Bhattacharya