  The Bunch-Davies state appears precisely thermal to a free-falling observer
in de Sitter space. However, precise thermality is unphysical because it
violates energy conservation. Instead, the true spectrum must take a certain
different form, with the Boltzmann factor $\exp(-\beta \omega_k)$ replaced by
$\exp(\Delta S)$, where $S$ is the entropy of the de Sitter horizon. The
deviation from precise thermality can be regarded as an explicitly calculable
correction to the Bunch-Davies state. This correction is mandatory in that it
relies only on energy conservation. The modified Bunch-Davies state leads, in
turn, to an ${\cal O} (H/M_p)^2$ modification of the primordial power spectrum
of inflationary perturbations, which we determine.
