  We discuss the subtle relationship between massive gravity and bimetric
gravity, focusing particularly on the manner in which massive gravity may be
viewed as a suitable limit of bimetric gravity. The limiting procedure is more
delicate than currently appreciated. Specifically, this limiting procedure
should not unnecessarily constrain the background metric, which must be
externally specified by the theory of massive gravity itself. The fact that in
bimetric theories one always has two sets of metric equations of motion
continues to have an effect even in the massive gravity limit, leading to
additional constraints besides the one set of equations of motion naively
expected. Thus, since solutions of bimetric gravity in the limit of vanishing
kinetic term are also solutions of massive gravity, but the contrary statement
is not necessarily true, there is not complete continuity in the parameter
space of the theory. In particular, we study the massive cosmological solutions
which are continuous in the parameter space, showing that many interesting
cosmologies belong to this class.
