Bursty star formation in dwarf galaxies can slowly transform a steep dark matter cusp into a constant density core .
We explore the possibility that globular clusters ( GCs ) retain a dynamical memory of this transformation .
To test this , we use the nbody6df code to simulate the dynamical evolution of GCs , including stellar evolution , orbiting in static and time-varying potentials for a Hubble time .
We find that GCs orbiting within a cored dark matter halo , or within a halo that has undergone a cusp-core transformation , grow to a size that is substantially larger ( R _ { eff } > 10 pc ) than those in a static cusped dark matter halo .
They also produce much less tidal debris .
We find that the cleanest signal of an historic cusp-core transformation is the presence of large GCs with tidal debris .
However , the effect is small and will be challenging to observe in real galaxies .
Finally , we qualitatively compare our simulated GCs with the observed GC populations in the Fornax , NGC 6822 , IKN and Sagittarius dwarf galaxies .
We find that the GCs in these dwarf galaxies are systematically larger ( \langle R _ { eff } \rangle \simeq 7.8 pc ) , and have substantially more scatter in their sizes , than in-situ metal rich GCs in the Milky Way and young massive star clusters forming in M83 ( \langle R _ { eff } \rangle \simeq 2.5 pc ) .
We show that the size , scatter and survival of GCs in dwarf galaxies are all consistent with them having evolved in a constant density core , or a potential that has undergone a cusp-core transformation , but not in a dark matter cusp .