  Motivated by their potential role as dark matter, we study the cosmological
evolution of light scalar and vector fields non-minimally coupled to gravity.
Our focus is on a situation where the dominant contribution to the energy
density arises from the misalignment mechanism. In addition, we also discuss
the possibility that dark matter is generated in a stochastic scenario or from
inflationary fluctuations. Even small deviations in the non-minimal couplings
from the standard scenarios lead to significant qualitative and quantitative
changes. This is due to the curvature-coupling driven superhorizon evolution of
the homogeneous field and the non-zero momentum modes during inflation. Both
the relic density yield and the large-scale density fluctuations are affected.
For the misalignment mechanism, this results in a weakening of the isocurvature
constraints and opens up new viable regions of parameter space.
