Measures in Mutlifield Inflation
  We examine the classical dynamics of multifield inflation models with
quadratic potentials. Such models are shown to have inflationary attractors in
phase space, consistent with the stretching of phase space trajectories along
the volume factor of the universe during inflation. Using the symplectic
structure associated with Hamiltonian systems we form a measure on the phase
space, as initially proposed by Gibbons, Hawking and Stewart. This is used to
calculate lower bounds on the probabilities of observational agreement (i.e.
the probability the model gives a value for the spectral index within the
region $n_{s}=0.968\pm{0.006}$) for equal mass two and three field models with
quadratic potentials, giving values of 0.982 and 0.997 respectively. We derive
the measure for a general $N$-field model and argue that as the number of
fields approaches infinity, the probability of observational agreement
approaches one.
