Interaction of cosmological domain walls with large classical objects,
  like planets and satellites, and the flyby anomaly
  Cosmological domain walls can be formed as a result of symmetry breaking at
any epoch during the evolution of our universe. We study their interaction with
a classical macroscopic object, like Earth or a satellite in Earth's orbit. We
set up an action that includes the interaction term between the massive
classical object and the scalar field that the domain wall is made of. We use
numerical calculations to solve the coupled equations of motion which describe
the crossing between the domain wall and the classical object. Depending on the
strength of the interaction, relative velocity and size, the object can be
either stopped by the wall, or it can pass through it inducing deformations in
the wall that cost energy. At the same time, the coupling to the scalar filed
might change the object's mass during the crossover. The fact that satellites
in Earth's orbit (or planets in Sun's orbit) can change their mass and/or lose
energy interacting with walls can be used as a new domain wall detection probe.
For example, a typical velocity precision of a satellite is about $0.5$ mm/s,
which directly puts an upper limit on its mass change to $\Delta M/M
\lessapprox 5\times 10^{-17} $. Alternatively, a known satellite flyby anomaly
can easily be explained as an interaction with a closed domain wall. We also
show that the presence of matter modifies the scalar filed potential and can
locally create a bubble of the true vacuum, and thus trigger the decay of the
false vacuum. For a critical bubble which is able to expand, such an
interaction with the domain wall must be strong enough.
