Some examples of irreducible homology 3-spheres that bound <b> smooth</b> contractible 4-manifolds are listed in the comment to problem 4.2 in <a href="http://math.berkeley.edu/~kirby/problems.ps.gz"> Kirby's problem list</a>, and all of them happen to occur among the <a href="http://www.maths.ed.ac.uk/~aar/papers/milnbries.pdf">
Brieskorn spheres</a> $\Sigma(p,q,r)$ modelled on $\widetilde{SL}_2(\mathbb R)$,
i.e. such that $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}<1$ (except for the standard $S^3$, of course). 

<b> Question.</b> Are there any known homology 3-spheres that bound smooth contractible 4-manifolds and are modelled on other geometries, e.g. NIL or the hyperbolic space?
   
EDIT: Glazner in the paper "Uncountably many contractible 4-manifolds" constructed some other examples but I cannot recognize the geometry. (Glazner's six page paper
is easily googlable by title, and it gives an explicit representation for the fundamental group, denoted $G_n$ on page 40).