  Identifying what broken symmetries are present in the cuprates has become a
major area of research. Many authors have reported evidence for so-called "$Q
\sim 0$" order that involves broken inversion, mirror, chiral, or time-reversal
symmetry that is uniform in space. Not all these observations are well
understood and new experimental probes are needed. Here we use resonant soft
x-ray scattering (RSXS) to search for $Q \sim 0$ order in
Bi$_{2.1}$Sr$_{1.9}$CaCu$_2$O$_{8+x}$ (Bi-2212) by measuring the region of a
forbidden Bragg peak, $(0,0,3)$, which is normally extinguished by symmetry but
may become allowed on resonance if valence band order is present. Using
circularly polarized light, we found that this reflection becomes allowed on
the Cu $L_3$ resonance for temperatures $T_c < T < T^\ast$, though remains
absent in linear polarization and at other temperatures. This observation
suggests the existence of spatially uniform valence band order near the
pseudogap temperature. In addition, we observed periodic oscillations in the
specular reflectivity from the sample surface that resemble thin film
interference fringes, though no known film is present. These fringes are highly
resonant, appear in all polarizations, and exhibit a period that depends on the
location where the beam strikes the sample surface. We speculate that these
fringes arise from interaction between some intrinsic valence band instability
and extrinsic structural surface morphologies of the material. Our study
supports the existence of some kind of $Q \sim 0$ broken symmetry state in
Bi-2212 at intermediate temperatures, and calls for further study using a
microfocused beam that could disentangle microscopic effects from macroscopic
heterogeneities.
