Density Perturbations from Two--eld Innation 1

We discuss metric perturbations produced during a period of innation in the early universe where two scalar elds evolve. The nal scalar perturbation spectrum can be calculated in terms of the perturbed expansion along neighbouring trajectories in eld-space. In the usual single eld case this is xed by the values of the elds at horizon-crossing, but in the presence of more than one eld there is no longer a unique slow-roll trajectory. The presence of entropy as well as adiabatic uctuations means that the super-horizon-sized metric perturbation may no longer be conserved and the evolution must be integrated along the whole of the subsequent trajectory. In general there is an inequality between the ratio of tensor to scalar perturbations and the tilt of the gravitational wave spectrum, which becomes an equality when only adiabatic perturbations are possible and is conserved. Innation was originally proposed as a mechanism to produce a at, isotropic and homogeneous universe. However it was soon realised that vacuum uctuations in a scalar eld driving innation would also lead to the production of an approximately scale-invariant spectrum of inhomogeneities. A good deal of progress has been made in understanding and parameterising generic features of the perturbation spectrum independently of the speciic interaction potential as long as it is driven by a single scalar eld 1]. Our intention here is to emphasise which features are restricted to models of a single eld evolving during innation and what happens when more than one eld is present 2, 3].