  In this work, we consider the possibility that wormhole geometries are
sustained by their own quantum fluctuations, in the context of modified
dispersion relations. More specifically, the energy density of the graviton
one-loop contribution to a classical energy in a wormhole background is
considered as a self-consistent source for wormholes. In this semi-classical
context, we consider specific choices for the Rainbow's functions and find
solutions for wormhole geometries in the cis-planckian and trans-planckian
regimes. In the former regime, the wormhole spacetimes are not asymptotically
flat and need to be matched to an exterior vacuum solution. In the latter
trans-planckian regime, we find that the quantum corrections are exponentially
suppressed, which provide asymptotically flat wormhole geometries with a
constant shape function, i.e., b(r)=r_t, where r_t is the wormhole throat. In
addition to this analysis, we also fix the geometry by considering the
behaviour of a specific shape function through a variational approach which
imposes a local analysis to the problem at the wormhole throat. We further
explore the respective parameter range of the Rainbow's functions, and find a
good agreement with previous work.
