  Universality is a powerful concept in physics, allowing one to construct
physical descriptions of systems that are independent of the precise
microscopic details or energy scales. A prime example is the Fermi gas with
unitarity limited interactions, whose universal properties are relevant to
systems ranging from atomic gases at microkelvin temperatures to the inner
crust of neutron stars. Here we address the question of whether unitary Bose
systems can possess a similar universality. We consider the simplest strongly
interacting Bose system, where we have an impurity particle ("polaron")
resonantly interacting with a Bose-Einstein condensate (BEC). Focusing on the
ground state of the equal-mass system, we use a variational wave function for
the polaron that includes up to three Bogoliubov excitations of the BEC, thus
allowing us to capture both Efimov trimers and associated tetramers. Unlike the
Fermi case, we find that the length scale associated with Efimov trimers (i.e.,
the three-body parameter) can strongly affect the polaron's behaviour, even at
boson densities where there are no well-defined Efimov states. However, by
comparing our results with recent quantum Monte Carlo calculations, we argue
that the polaron energy is a \emph{universal} function of the Efimov three-body
parameter for sufficiently low boson densities. We further support this
conclusion by showing that the energies of the deepest bound Efimov trimers and
tetramers at unitarity are universally related to one another, regardless of
the microscopic model. On the other hand, we find that the quasiparticle
residue and effective mass sensitively depend on the coherence length $\xi$ of
the BEC, with the residue tending to zero as $\xi$ diverges, in a manner akin
to the orthogonality catastrophe.
