  Inflation universally produces classical almost scale free Gaussian
inhomogeneities of any light scalars. Assuming the coupling constants at the
time of inflation depend on some light moduli fields, we encounter the
generation of modulated cosmological fluctuations from (p)reheating. This is an
alternative mechanism to generate observable (almost) scale free adiabatic
metric perturbations. We extend this idea to the class of hybrid inflation,
where the bifurcation value of the inflaton is modulated by the spatial
inhomogeneities of the couplings. As a result, the symmetry breaking after
inflation occurs not simultaneously in space but with the time laps in
different Hubble patches inherited from the long-wavelength moduli
inhomogeneities. To calculate modulated fluctuations we introduce techniques of
general relativistic matching conditions for metric perturbations at the time
hypersurface where the equation of state after inflation undergoes a jump,
without evoking the detailed microscopic physics, as far as it justifies the
jump. We apply this theory to the modulated fluctuations from the hybrid and
chaotic inflations. We discuss what distinguish the modulated from the
inflation-driven fluctuations, in particular, their spectral index,
modification of the consistency relation and the issue of weak non-Gaussianity.
