  Motivated by slow-roll inflationary cosmology we study a scalar unparticle
weakly coupled to a Higgs field in the broken symmetry phase. The mixing
between the unparticle and the Higgs field results in a seesaw type matrix and
the mixing angles feature a Mikheyev-Smirnov-Wolfenstein (MSW) effect as a
consequence of the unparticle field being noncanonical. We find two (MSW)
resonances for small and large spacelike momenta. The unparticlelike mode
features a nearly flat potential with spinodal instabilities and a large
expectation value. An effective potential for the unparticlelike field is
generated from the Higgs potential, but with couplings suppressed by a large
power of the small seesaw ratio. The dispersion relation for the Higgs-like
mode features an imaginary part even at "tree level" as a consequence of the
fact that the unparticle field describes a multiparticle continuum. Mixed
unparticle-Higgs propagators reveal the possibility of oscillations, albeit
with short coherence lengths. The results are generalized to the case in which
the unparticle features a mass gap, in which case a low energy MSW resonance
may occur for lightlike momenta depending on the scales. Unparticle-Higgs
mixing leads to an effective unparticle potential of the new-inflation form.
Slow-roll variables are suppressed by seesaw ratios and the anomalous
dimensions and favor a red spectrum of scalar perturbations consistent with
cosmic microwave background data.
