Typical properties of periodic Teichmuller geodesics: Lyapunov exponents

Consider a component Q of a stratum in the moduli space of area-one abelian differentials on a surface of genus g. Call a property P for periodic orbits of the Teichmuller flow on Q typical if the growth rate of orbits with property P is maximal. We show that the following property is typical. Given a continuous integrable cocycle over the Teichmuller flow with values in a vector bundle V -> Q, the logarithms of the eigenvalues of the matrix defined by the cocycle and the orbit are arbitrarily close to the Lyapunov exponents of the cocycle for the Masur-Veech measure.