GRB$\,$220831A: a hostless, intermediate Gamma-ray burst with an unusual optical afterglow

GRB$\,$220831A is a gamma-ray burst (GRB) with a duration and spectral peak energy that places it at the interface between the distribution of long-soft and short-hard GRBs. In this paper, we present the multi-wavelength follow-up campaign to GRB$\,$220831A and its optical, near-infrared, X-ray and radio counterparts. Our deep optical and near-infrared observations do not reveal an underlying host galaxy, and establish that GRB$\,$220831A is observationally hostless to depth, $m_i\gtrsim26.6$ AB mag. Based on the Amati relation and the non-detection of an accompanying supernova, we find that this GRB is most likely to have originated from a collapsar at $z>2$, but it could also possibly be a compact object merger at $z<0.4$ with a large separation distance from its host galaxy. Regardless of its origin, we show that its optical and near-infrared counterpart departs from the evolution expected from a forward shock dominated synchrotron afterglow, exhibiting a steep post-break temporal powerlaw index of $-3.83^{+0.62}_{-0.79}$, too steep to be the jet-break. By analysing a range of models, we find that the observed steep departure from forward shock closure relations is likely due to an internal process producing either a flare or a plateau.