  Through the Gertsenshtein effect, the presence of a large external B-field
may allow photons and gravitons to mix in a way that resembles neutrino
oscillations and is even more similar to axion-photon mixing. Assuming a
background B-field (or any field that behaves like one), we examine the
Gertsenshtein mechanism in the context of FLRW expanding universe models, as
well as de Sitter space. The conformal invariance of Maxwell's equations and
the conformal noninvariance of the Einstein equations preclude the operation of
the Gertsenshtein effect at all scales. In general we find for the matter- and
radiation-dominated cases, graviton-oscillations are possible only at late
conformal times or when the wavelengths are much shorter than the horizon
($k\eta \gg 1$), but that the time-dependent oscillations eventually damp out
in any case. The presence of charged particles additionally damps out the
oscillations. For the de Sitter universe, we find that oscillations are
possible only at early conformal times ($\eta \ll H^{-1}$) and for wavelengths
short compared to the Hubble radius, but eventually freeze in when wavelengths
become longer than the Hubble radius. In principle a Gertsenshtein-like
mechanism might influence the balance of particle species in an inflationary
phase before freezing in; however, we find that in all our models the mixing
length is larger than the Hubble radius. We discuss several possible remedies
to this situation.
