  Inflationary cosmology predicts a low-amplitude graviton background across a
wide range of frequencies. This Letter shows that if one or more extra
dimensions exist, the graviton background may have a thermal spectrum instead,
dependent on the fundamental scale of the extra dimensions. The energy density
is shown to be significant enough that it can affect nucleosynthesis in a
substantial way. The possibility of direct detection of a thermal graviton
background using the 21-cm hydrogen line is discussed. Alternative explanations
for the creation of a thermal graviton background are also examined.
