Coboundary expansion conjecture for Ramanujan balanced Cayley complexes

Let $p$ and $q$ be distinct odd primes with $q>2\sqrt p$ and Legendre symbol $\left(\frac pq\right)=1$, let $G_q=\operatorname{PSL}_2(\mathbb{F}_q)$, and let $S_{p,q}\subset G_q$ be the subset of cardinality $p+1$ arising from the Lubotzky–Phillips–Sarnak Ramanujan graph construction. Let $Y_{S_{p,q},k}$ be the associated balanced Cayley complex, and let $h_{k-1}$ denote its $(k-1)$-st coboundary expansion constant. Coboundary expansion conjecture for Ramanujan balanced Cayley complexes. For any fixed $k\geq 1$ there exist constants $p_0(k)<\infty$ and $\epsilon_0(k)>0$ such that if $p>p_0(k)$, $q>2\sqrt p$ and $\left(\frac pq\right)=1$, then

$$h_{k-1}\left(Y_{S_{p,q},k}\right)\geq\epsilon_0(k).$$

This is proposed as a coboundary-expansion analogue of the established spectral-gap estimate for these complexes. The source gives no resolution of the conjecture.