  The inclusive photon energy spectra measured by the Large Hadron Collider
forward (LHCf) experiment in the very forward region of LHC proton-proton
collisions at $\sqrt{s}=$ 900 GeV are reported. The results from the analysis
of 0.30 $\mathrm{nb^{-1}}$ of data collected in May 2010 in the two
pseudorapidity regions of $\eta > 10.15$ and $8.77 < \eta < 9.46$ are compared
with the predictions of the hadronic interaction models DPMJET 3.04, EPOS 1.99,
PYTHIA 8.145, QGSJET I -.1em I-03 and SIBYLL 2.1, which are widely used in
ultra-high-energy cosmic-ray experiments. EPOS 1.99 and SYBILL 2.1 show a
reasonable agreement with the spectral shape of the experimental data, whereas
they predict lower cross-sections than the data. The other models, DPMJET 3.04,
QGSJET I -.1em I-03 and PYTHIA 8.145, are in good agreement with the data below
300 GeV but predict harder energy spectra than the data above 300 GeV. The
results of these comparisons exhibited features similar to those for the
previously reported data for $\sqrt{s}=$ 7 TeV collisions.
