  We demonstrate that loop integrands of (super-)gravity scattering amplitudes
possess surprising properties in the ultraviolet (UV) region. In particular, we
study the scaling of multi-particle unitarity cuts for asymptotically large
momenta and expose an improved UV behavior of four-dimensional cuts through
seven loops as compared to standard expectations. For N=8 supergravity, we show
that the improved large momentum scaling combined with the behavior of the
integrand under BCFW deformations of external kinematics uniquely fixes the
loop integrands in a number of non-trivial cases. In the integrand
construction, all scaling conditions are homogeneous. Therefore, the only
required information about the amplitude is its vanishing at particular points
in momentum space. This homogeneous construction gives indirect evidence for a
new geometric picture for graviton amplitudes similar to the one found for
planar N=4 super Yang-Mills theory. We also show how the behavior at infinity
is related to the scaling of tree-level amplitudes under certain multi-line
chiral shifts which can be used to construct new recursion relations.
