  We performed a fluctuation analysis of the Hubble Extremely Deep Field (XDF)
at four optical wavelength bands and found large fluctuations that are
significantly brighter than those expected for ordinary galaxies. Good
cross-correlations with flat spectra are found down to 0.2 arcsec, indicating
the existence of a spatial structure even at the 0.2 arcsec scale. The detected
auto and cross-correlations provide a lower limit of 24 nW m$^{-2}$ sr$^{-1}$
for the absolute sky brightness at 700-900 nm, which is consistent with
previous observations. We searched for candidate objects to explain the
detected large fluctuation using the catalog of the Hubble Ultra Deep Field
(UDF), and found that the surface number density of faint compact objects
(FCOs) rapidly increases toward the faint end. Radial profiles of FCOs are
indistinguishable from the PSF, and the effective radius based on de
Vaucouleur's law is estimated to be smaller than 0.02 arcsec. The SEDs of FCOs
follow a power law at optical wavelengths, but show greater emission and
structure at $\lambda$ > 1 $\mu$m. Assuming that the FCOs are the cause of the
excess brightness and fluctuations, the faint magnitude limit is 34.9 mag for
the F775W band, and the surface number density reaches $2.6 \times 10^3$
(arcsec)$^{-2}$. Recent gamma-ray observations require that the redshift of
FCOs must be less than 0.1, if FCOs are the origin of the excess optical and
infrared background. Assuming that FCOs consist of missing baryons, the mass
and luminosity of a single FCO range from $10^{2}$ to 1$0^{3}$ solar units, and
mass-to-luminosity ratio is significantly lower than 1.0 solar unit. The
maximum effective radius of an FCO is 4.7 pc. These results and the good
correlation between near-infrared and X-ray background indicate that FCOs could
be powered by the gravitational energy associated with black holes.
